Algebra AGE WORD PROBLEM - Let’s solve it step-by-step...

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Math help with algebra word problem involving age. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at tcmathacademy.com/
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[@jarmstrong2843]

I am a retired mechanical engineer and quantum physicist with a PhD in both fields. I was a research scientist in both the space and arms development fields. Mathematics were my entire life. However, four years ago I suffered a stroke. Now my mathematical abilities are no longer there. I struggle with the basic concepts. Even many of my writing abilities are much less than they were. I view your videos quite often, but what I learned today will have to be relearned tomorrow. And so goes the struggle each day. The Drs don’t seem to think I will ever recover in many respects. But, I will keep plugging away until some day the connections are made. Thanks for your videos. They do help, but in my case in small increments.

[@clarkhull7546]

Hang in there you'll get back to your old self.

[@annatygrys9043]

Keep on it Brother and pray to God, than the miracle will happen! 90% of miracles happen in our mind! The Holly Spirit cleans our mind from fear and pessimistics thoughts, than anything turns out very easy. Greetings!

[@tonylaut585]

If I may ask, how old are you. My situation is similar and I'm 65. I don't think there are many years left to go. I too was in the military weapons development industry here in Canada (ya, we did that stuff too up here in the great white north. Most of my stuff was Navy based defence related. Back in 2008 I suffered s heart attack and had to re-learn so much stuff. But a lot of math related stuff never got back on track especially the high end stuff. 😎🇨🇦

[@jodygotyourgirlngone]

Well...you could always get into porn acting...tee hee hee hee....

[@simmo5071]

Had a similar problem 12 years ago, I watch because making change was tough. Time as they say and for once they’re correct is the great healer. I’m 69 yrs old trying to get a golf game back. Good luck to you staying positive really, really helps.

[@richardowens9061]

I would have solved for the age Beth would be next year. And, since we know Beth would be twice her brother's age next year, we can simply take the eight year difference and multiply that by two to get 16. Then, just subtract one to get Beth = 15 years old right now.

[@commonleadership48]

Perfect logic and without all the BS from the presenter, 15 minutes of lecture and patronizing to get to the point.

[@chrisprice2485]

Exactly how i solved it.....in like two seconds. No formula or charts necessary.

[@dragonan5674]

Plus there is only one year where she would be twice her brothers age with that difference in age.

[@jolenedouglas3207]

If the kids listened. or read the problem it would have jumped out at them

[@MrBawdry]

This seemed so obvious. 8 x 2. Then subtract 1.

[@ATCguy1973]

Thank you for reminding me why I dropped out of highschool. Teachers always tested patience by talking too much!

[@SifuFreeGamer1417]

Facts

[@kaviarkodell1914]

Omgggg thank you

[@Elsie64]

But do you know the answer

[@jackspeer2127]

Right on.

[@trailertrish2587]

I dropped out for other reasons but math was my favorite subject when I was there.

[@community-fusionnetwork4131]

She's 15 and he's 7. Next year, she'll be 16 and he'll be 8. I'm not a math genius, but I can figure that out in my head

[@footloose6382]

Me too😊

[@community-fusionnetwork4131]

@@footloose6382 it's something like (x + 8) × 2 = (x + 2) + 1. Is that correct?

[@community-fusionnetwork4131]

@@footloose6382 i meant (x + 8) + 1 on the second half of the equation

[@community-fusionnetwork4131]

Oh it's x MINUS 8

[@community-fusionnetwork4131]

Look at me, I'm talking to myself like a crazy person 🤪

[@jwac3io]

1. Please get to the point. 2. Give students a massive tip: You read the call of the question line first. I.E. "How old is Beth now?" OMG! Beth will be eight years older than her brother next year as well as this year. x+8=2x. Solve for X. X=8. Next year B and B will be 16, and 8. Subtract one for this year: Beth is 15. Brother is 7. For heaven's sake.

[@belladriver258]

Why are you here? I’m here because I got 18 lol I suck at math

[@lookingforahookup]

You talk too much you bore us who watch the video.

[@Fan-qu8qy]

Read the question

[@CouponFrenzy]

That's how I solved it too. 😁

[@ramcatracer]

Yup. I figured it out in about 7 1/2 seconds! Of course that is her brothers age in years. Or 236520000 seconds, haha! But you're right. This just puts people off as in...what a joke. My Algebra teacher filled a board with equations while I was day dreaming. I looked up and raised my hand. Why don't you just double it and subtract one? (Or something like that) He was hopping mad, spent the rest of the hour trying to prove me wrong. He was jubilant when it didn't work for zero or maybe one. So I said ok there's an exception to the rule, happens all the time! Class loved it, called it the Bensonian Theorem. Still good at math but terrible at Algebra and Geometry. Designer- Inventor by trade. No problems! Sorry author. Choose something that truly is perplexing to begin with? JMO

[@ldavery100]

She aged 10 years waiting for him to get to the point! GET TO THE POINT!

[@gregoryharlston0602]

Beth was 15 when this video started and 16 when he finished!

[@bman5333]

AGREED! This teacher has a great smooth voice quality, rhythm, monotone and voice inflection for reading bed time stories. It worked on me after about four minutes. Listen to him when you go to bed and you might not learn wur proms however, you will doze off quickly. I never had a problem with wur proms (listen to him say it) and I did not use a convoluted process. I went to college a little later in life and I made an A in college algebra with a professor who told us 'if you were going to be math majors you would not be in this class'. So he used examples that had daily practical applications. Prior to college I was a welder/fabricator and I used algebra on a daily basis but I had a practical application for it.

[@adammiller2246]

LOL I spit my coffee out when I read your post!!!

[@bryanlane3713]

I watched one or two of his videos and gave up on him.

[@mountainmanws]

@@bryanlane3713 agree. The Indian math teacher on KZbin could have solved this problem with thorough understanding in three minutes.

[@imagewavesurfphoto4567]

At 4 minutes in I derived that this guy is the kind of teacher that turns kids off to math. HE NEVER SHUTS UP AND GETS TO THE POINT…!!!!

[@sismos88]

exactly

[@pamelalaw7575]

Then watch other people videos or make you own .... For anyone who is just starting needs all the info that they can so the Information can sink in....

[@sismos88]

@@pamelalaw7575 just make it a two hours video/explanation then, or even more.

[@johnspence8141]

hes posting click bait math too for views

[@dswynne]

@@sismos88 If you can't contribute to the learning process, move on.

[@jeffburnham6611]

The reasons students get distracted is because the teachers spend too much time rambling on about non-essential information not relevant to the equation. I had a teacher like that. He would spend 30-45 minutes talking about how to solve a different equation, or what a variable i, etc. He then would rattle off a new equation for 5 minutes and then turn the class loose with the assignment as homework. Always wanted to see the work for each equation. The only people that liked math were the ones that could solve the problem in their head, and just wrote down the equation as they went. I was glad when the semester ended. I hated Algebra, still do. My life goals didn't include a job at NASA, JPL, or anywhere in the scientific field.

[@jmcd9255]

Sounds as though you just didn't want to learn. The teacher spent a bit of time and you didn't appreciate it.

[@lorrieprothero2175]

Agreeeeeddddd!

[@robertnorthrup1914]

And this guy is doing it too. Just cut the crap and do it.

[@kfl611]

I got a 27 on an algebra test - did anyone care? NO, they could all care less that I was totally lost in the subject and beyond clueless. Ha ha ha. My mom got placed in an advanced math class in college, since she did so well in Algebra in highschool. Go freaking figure.

[@jodygotyourgirlngone]

So...how's the McJob been for you, then?

[@jerrygustanski419]

I am a retired computer programmer and I set up two equations: 1: x = y - 8 and 2: y + 1 = 2(x+1). Substituting the 1st y - 8 into the second for x allows you, after moving things around, to solve directly for y. I just wanted to see if I could still do it at age 71+.

[@davidroddini1512]

I did something similar except my first equation was x+8=y and plugged that into the second equation to solve for x directly, then added 8 to get the Beth’s current age.

[@gabrielferdinand9070]

I am

[@rockyraccoon8270]

@@davidroddini1512 That is what I did too.

[@OhJodi69]

When Beth finishes this video, she will feel much more than 8 years older than her brother.

[@bettybumbledust]

So funny

[@juniorferrante7999]

Hysterical. First and last time I’ll watch this guy’s videos. At around 9:22 he finally says ok let’s look at this problem

[@hot88s23]

They both will have died of old age.

[@johnalanelson]

And yet, in all likelihood will still be only 14!

[@johnalanelson]

@@bettybumbledust It is funny that he makes it sound so hard, yet still comes up with an answer that is probably wrong!

[@manofmartin]

My daughter, at age 16, asked me for help with math. I used to be very fluent in algebra. I was stumped almost instantly. I've been combing through all your algebra play lists to refresh. It's amazing what you forget over 20 years. Thank you for taking the time for what is likely a lot of moms and dads trying to help their kids 20+ years later!

[@alianjohnson6035]

Mate I've said before that there is too much 'talk' in the video - 5 mins in and we haven't started the problem. this is a 5 min video so appreciate it if you can keep them brief and not try and push the content and 'extras' out to 20 min. please look at the comments below

[@jeffreylonigro1382]

Agreed. I’d watch more of these but it takes him forever to get to it.

[@ffgrif]

I had it solved before the ads were even done! LOL!

[@lorrieprothero2175]

After three minutes of him talking about nonsense i shut off the video. I saw no point in searching for actual content. Basically i got bored

[@johnalanelson]

It seems like a good lesson in how to do things the hard way! The math is valid, but unnecessarily complicated, and the logic is flawed. She is 8 years older than her brother and will be twice his age next year so 2x8=16, next year she will be 16. The question is: *how old is she now?* That's the flaw in the logic. She will be 15 this year, but we don't know if she has had her birthday yet this year so her age *now* could be either 15 or 14. Since it was posted on Jan 12, she most likely has *not* yet had her birthday, so is still only 14.

[@joepalmer3208]

I did it in my head in 2 seconds. Next year she'll be double her brother's age, so Beth is 15 and her brother is 7. However, I can see where the algebra would be needed if the question were more complex. Good video!

[@janettamcgee8124]

Yeah, same thing here.

[@ffgrif]

Same here!

[@gerardjlaw]

I presume you doubled eight to get sixteen? Why??? Granted, your answer matches the correct answer, but that's just a coincidence caused by the brother's age (the thing you SHOULD have multiplied by two) being the same as the age differential (the number you actually - but mistakenly - multiplied by two). Not convinced? Try it with Beth being THREE times her brother's age. Do I hear the words, "She'll be twenty-four." wafting this way? That IS what your reasoning demands, but it's wrong. In fact, she'll be twelve, as the algebra makes clear.

[@gerardjlaw]

@@janettamcgee8124 In that case, you may want to have a look at my analysis above.

[@gerardjlaw]

@@ffgrif In that case, you may want to have a look at my analysis above.

[@thinkingoutloud6741]

For every exam I took throughout my undergrad degree work in mathematics, I started each by writing across the top page of my answer, in large capital letters RTFQ. It was a great reminder. Thanks for passing along the importance of reading the question.

[@peteherrera1502]

and I say The story is not possible since a person cannot be twice as old as their brother using the example described above. This is an example of a Terribly worded English Math problem. No wonder why a lot of people hate math word problems. The first part was fine. if her brother was 1 she would be 9. Reading bad english does not change the fact that it is bad english

[@maggiepatterson7949]

Really starts at about 5:32...if you are interested.

[@alwandedlamini9528]

You lie😮‍💨😮thank you, really helped

[@lennartbjorksten707]

In word problems, start by making your variable equal to the answer. Let x be how old Beth is now. Her brother is then (x-8) years old. Next year, Beth's age will be (x+1). Her brother's will be (x-8)+1, or x-7. So (x+1) = 2*(x-7). Solving for x, we get x = 15. Answer: Beth is now 15 years old. Double checking: Beth is 15 and her brother is 7. Next year, her brother will be 8 and Beth will be 16, which is twice her brother's age. Yep, checks out. Why did this take 21 minutes?

[@duncantoms]

I agree about your method and I’m 10. Thank you

[@3dbadboy1]

It took 21 min because of exposition and explanation.

[@dcrtse]

Thank you for the video. However, and I say this with all due respect, I have to agree with others that there was too much talking to show the steps and how to solve this problem. I found myself losing interest almost immediately and had to fast forward the video. Perhaps cut down on the chatter and get more to the point would be helpful? On a more positive note, it appears you are the kind of teacher who loves to teach, is patient, and is willing to answer a gazillion questions from students. Thank you for sharing your knowledge!

[@MPam1619]

Somewhere along the way, years ago, i didn't learn (in sequence) the skills i should have learned before being introduced to algebra. Consequently, math became a dreaded and least favorite subject for me by high school. Ironically, i was 1 of only 2 students who successfully passed a real estate sales math course out of a group of 24 adults years later. And, i LOVED the math portion of the exam. I just think my family moved a bit too much during my elementary school years and it caused me to lose out on sequential math instruction. In other words, thanks every so much for your video!

[@kfl611]

English parts of speech (gerunds, nominatives, dative etc.) and algebra never made much sense to me. I was always so lost in school when they were teaching these subjects. I think it was partly due to moves too - as I got dumped into the middle of the subjects, having never seen them before.

[@gregoryharlston0602]

I like that you are engaging and thorough, but math videos over 5 minutes don't get viewed nearly as often as shorter videos. I like the table you created (9:32) with the variables and I think it will help many struggling students. The main problem is that most of these struggling students would probably have clicked on another video before they get to these tables.

[@Ososedavid]

yes brother

[@kiki64allen56]

no wonder I was always useless at algebra. I have never watched such a long winded video in my life! I had the answer of 15 in about 15 seconds just reading the problem but never would I have sorted out all your working out. I have a block on finding the easy way to do anything, always have but with algebra would read problem and solve in 30 seconds but could never understand the reason for the long working out of it. Drove my maths teacher crazy and my physics teacher would laugh and say my brain was weird because I always knew the answer without having to sit and work it out. I get where you are coming from but I don't see the point of all those workings out for nothing.

[@markcharles776]

I'm with you bud teachers are long winded , I guess they have to justify there positions in the teaching world .

[@gerardjlaw]

The working out isn't "for nothing". You can only do this problem informally (sometimes known as "solving by inspection") when the figures are childishly simple. What if Beth were eighteen years older and had been four times her brother's age five years ago? Or eighteen and a half years older, and and will be one and a half times his age in seventeen years? (Answers: twenty-nine & eleven and thirty-eight and a half & twenty.)

[@logannaidoo1]

Though he's warm and articulate, I find his teaching style to be long and drawn out. Advice which can be confined to the end are interspersed with the explanation, causing one to lose one's focus and concentration. Which, for a subject like Math, is not ideal. Cut to the chase, sir. Life's short enough as it is.

[@lorrieprothero2175]

Yup. Just do the problem. Stop talking about everything but the problem

[@johnalanelson]

The question as stated has two equally valid answers, and the one he gave is the least likely of the two.

[@rev.markcarrier1894]

He doesn’t actually start solving the problem until the 9 minute 27 second mark.

[@cathylarkins9949]

This is the type of teacher who would help me catch up on my sleep deprivation

[@weremodel]

Been awhile, this was a good review! 64 year old carpenters listen, take notes and pay attention. Thank you, Jim Bauer.

[@louisd95714]

I wish I had this guy as a Math teacher in high school! When my daughter started college this is exactly one of the word problems she came across, and I always struggled with these word problems myself.

[@skilz8098]

High school? We were doing these in 3rd grade... well maybe 4th...

[@irProteus]

This is a classic example of VERBOSITY; with a teacher like this I would have RUN out of the classroom with my hands over my ears S C R E A M I N G.... and NEVER returning!

[@trevorcarlisle5447]

Thank you! This made my day and I feel a lot smarter knowing I was justified in the end having the right answer. This would make my elementary self proud. Subscribed!

[@johnburgess2084]

Very nice. My math teachers (don't remember the year) required a Step 7, check your answer. Substitute your solved value for X in the 2nd row and see if that is true. 16 is twice 8, so check!

[@MaeMae-vg8wo]

I am 75 y/o, and when I started school it wasn’t considered for girls to be taught the math and sciences. Sad but true. After all all you were going to do is get married and have children. I struggled with math for most of my years in school, which really makes a person feel stupid. I did end up going to college my my children were preteens. I obtained my AA, BA and MS degrees. Fortunately in my Masters program I had an excellent in teaching me statistics for behavioral sciences which I remembered long enough to to pass my finals. As time went on I started teaching myself math, as I am the kind of person who doesn’t like not accomplishing things that had been difficult for me in the past. I must say my brain kind of tilts when it comes to advanced math, but I haven’t given up. I am still working on accomplishing the advanced maths and the kind of help programs like yours have really helped me. So to all those dinosaurs of old, we old woman who were all made to feel “stupid” and unimportant with little value na na boo boo,

[@gerardjlaw]

Leaving aside for a moment the monstrous injustice of that situation, just think how many skilled scientists and engineers society was willing to forego in order to preserve its blinkered attitude to the advancement of women.

[@wRAAh]

You avoid the risk of mixing up Beth and her brother if you start by first defining that Beth's age = x and her brother's age = y. Then: a) y = x-8 (Brother's age is Beth's age minus 8 years), and b) x+1 = 2(y+1) (Next year Beth is twice the brother's age) -> x+1 = 2y+2 -> x = 2y+1 Substituting y for x-8 gets you: x = 2(x-8)+1 -> x = 2x-16+1 -> x = 15 Thus Beth(x) = 15 and brother(y) is 15-8 = 7 This way, your first answer is the thing that was asked for (Beth's age now) and knowing the brother's age is just a bonus, handy for checking if the outcomes are correct. I find this method a bit more safe, logical and elegant. And that's what maths is all about, right?

[@austfox2170]

Beth could also be 17. It says next year, not in 12 months. Beth's birthday might be in January and her brother's in March. So next year in January and February she could be 18 and her brother still 9!

[@kfl611]

Wait where is the train leaving from Chicago going 60 mph, trying to meet a bus going 70, and where will they meet?

[@austfox2170]

@@kfl611 The train is very close to Chicago, because you said 'leaving' not 'left'. Provided the bus stays within the road rules, the train and bus will never meet. Even at a level crossong, they will always be segregated.

[@edcones2948]

I figured she'd still be 8 years older than her brother next year, so twice as old then would have her 16 and him 8. So this year, her 15 and him 7. I'm not sure if I did it the same way they did or not, but it was logical. :)

[@gerardjlaw]

Why would she be sixteen? Because that's twice eight? Now try that theory with her being THREE times the brother's age. Will she be twenty-four? (Spoiler alert - she won't.)

[@webworm13]

Yes, you took a long time to explain the solution. This forced me to FOCUS. Your love of math is contagious. Now, I shall practice linear equations. I was thoroughly engrossed and encouraged by your explanation. If I choose to hang with friends instead of practicing, I may as well quit now. Thank you

[@richardbailey2001]

Never have I come across a person that likes the sound of his own voice so much... Is it any wonder that I didn't finish watching this video.

[@freddukepoo3359]

I had that equation figured out in my head in about 10 sec & it took 21 long minutes to find out i was right.

[@justinstephenson9360]

This is trivial and can be done in your head but the formula is easy as well. Set Beth's age =x and brother's age as y. From the question we know: 1) x=y+8 2) x+1=2(y+1) Lets expand out equation 2: x+1=2y+2, now simplify by subtracting 1 from both sides which results in the equation x=2y+1. Now substitute that result for x back into the first equation which gives you 2y+1=y+8, which simplifies down (by subtracting y+1 from both sides) to y=7. Substitute y=7 back into equation 1 gives you x=7+8, so x=15 and hence this year Beth is aged 15. You do not need 20+ minutes to explain that even to a 7 year old child

[@toddstevens13]

It takes less then a minute to figure this out without any sort of equations etc. Common Sense leads one to 15, quickly. Add divide multiple simple

[@pcmjpcmj6854]

What is trivial and easy for some is complicated for others.

[@riversong6216]

I totally agree! I was so busy skipping through all the verbiage that I never did hear the answer. I've never had any algebra as it was not required when I was in school (I'm in my 60's and have a Bachelor's degree) but I figured it out just by using common sense. I kept listening just to find out if I was right but he talked so much that I missed the answer. I'm glad I never had to take math under him. I would die of monotony!!!! I don't have time for all the fluff!

[@billfitzpatrick6202]

When my 5yr old son in kindergarden and I were talking about birthdays yrs ago, I asked him when he would be my age how old would I be, he almost immediately said 71, it took me about 20 seconds to prove him right, we made up math games to pass the time on any trips we made, it paid off big time, and he has always made me proud, I'll be 71 this year and this is one of my favorite memories!.....Some brains are wired for language and others numbers, quite a few neither and very, very few both!

[@stuartyoung4716]

During the lecture I worked on the problem and got the same answer using a slightly different approach. I saw that there were two unknowns, so I set up a system of two simultaneous and independent linear equations which reduced to a single equation that was the same as yours. Therefore my answer agreed with yours

[@talkingtrashtom]

For people being sarcastic, he is showing basics for approaching a word problem, so many have issues with the words, not seeing just numbers.

[@georgesadler7830]

MR. TabletClass Math , thank you for a classic analysis and explanation of Algebra Age Word Problem in old fashion high school algebra. Word problems are fun to solve in mathematics.

[@rogercline5377]

I agree that a good fundamental understanding of the math involved is important, and I agree that it's probably what's *most* important to Mr. TCM's target audience. At some point, it's good to delve in and begin playing around with the numbers, understand how and why math works. With a little understanding you can get to the correct solution much more elegantly and without going through each rote step. This is true in a lot, albeit not all, math problems.

[@bman5333]

No they're not. ;)

[@brucesmith9144]

Not only is it important to take good notes, but also to continually practice problem solving. For subject mastery and good preparation for exams (and usually higher grades) do *more* problems than were assigned for homework.

[@skilz8098]

I barely did any homework, and I would still ace the math courses blindfolded at least until trig... then I had to actually start paying attention a little bit. If you can remember your times table up to at least 12 and know how to factor then the rest is just remembering the equations and knowing when and where to use them. The biggest mistake that most people make that brings their grades down is forgetting to factor out a (-1). I've seen it too many times! Even in Calc classes. It's the little and simple things that will trip you up.

[@nerisaj]

You truly do have the best math online courses! It has been such a helpful review as I return to college after graduating HS many years ago. Thank you for creating an amazing online program!

[@Beejay129]

A nice 23 minutes. I use outcome based thinking in my sales courses. Start at your arrival point and work back to reach the result.😄

[@stevedavenport1202]

Pretty self explanatory, but most people don't think that way.

[@royarchibald6392]

I had the answer in about 15 seconds, but the algebra lesson brought back memories.

[@gerardjlaw]

You had AN answer, but was it the correct answer or a wrong answer that was numerically identical to the correct one??? I presume you doubled eight to get sixteen? That's Beth's age all right but that's just a coincidence caused by the brother's age (the thing you SHOULD have multiplied by two) being the same as the age differential (the number you actually - but mistakenly - multiplied by two). Not convinced? Try it with Beth being THREE times her brother's age. Do I hear the words, "She'll be twenty-four." wafting this way? That IS what your reasoning demands, but it's wrong. In fact, she'll be twelve, as the algebra makes clear.

[@uniqueplatypus7435]

@@gerardjlaw what do you mean? Its common sense, the only way for it to be correct is if she was 16, and anyone who solve this question easily could just as easily get 12, because its impossible for it to be any of the number.

[@gerardjlaw]

@@uniqueplatypus7435 Why do you need to ask what I mean? I've explained very thoroughly and unambiguously that it's very easy to make a fundamental mistake in the logic of solving this problem (in fact, by using what you describe as "common sense") but that that fundamental error gets hidden when Beth is twice her brother's age (rather than any other multiple), because then the erroneous answer comes out to be numerically the same as the correct answer. I note that you give no explanation for how to solve either the stated problem or my modified version. (And for the avoidance of doubt, "it's common sense" and "it's impossible for it to be anything else" are not generally accepted by the mathematics community as a formal proof.)

[@marcysikes]

Yes it is easy to figure out without going through all of this but the point of the video is to solve the problem through using algebra. Thank you for this video to make the basics understandable!

[@timsullivan4687]

Try using your brain and logical thinking instead

[@leftovertech]

I totally agree with Marcy. The point of the problem as presented is not really to figure out some little girl's age. If you understand the CONCEPT and its application, you can use it in countless more complex scenarios.

[@dlkline27]

As an example of how important it is to read and understand the problem, in high school I once was the only one in our algebra class to properly solve a written problem. Everyone in class had the same answer and I got into a rather heated argument with my best friend while in study hall but I stuck to my reasoning. READ THE PROBLEM and properly analyze it.

[@BrazosSteve]

I gave you a 👍 for the video containing an interesting problem and an “F” for being garrulous in your instruction on how to solve it. 🧐

[@jimbauer5560]

Been awhile, this was a good review! Young people listen, take notes and pay attention

[@richardlapinski8303]

The point is to assume the listeners knows absolutely nothing. So he is taking us thru it step by step. If you already know how to do it, and don’t need the step by step process? Kudos to you! Some of us need it though!

[@MichaelBuck]

I found 4 ways to solve this problem, one of which was your method, and all worked fine depending on your perspective and whether or not you chose 1 or 2 variables, and which variable you assigned to Beth and her Brother. For me I wanted to solve for BETH, so assigned the variable "X" to her. I assigned the variable "Y" to her brother. Reading part 1 of the problem we have: X = Y+8 Beth(X) is 8 years older than her brother (Y). Reading part 2 of the problem we have: X+1 = 2(Y+1) Next year Beth(X+1) will be twice (2) as old as her brother (Y+1). Then decide which variable you want to solve for, either variable will work and substitution will be required to get the equation to use all of the same variable. If you solve for her BRother "Y" you will have an additional step of then solving for Beth. In this case, I solved for BETH or "X" as that is what the problem required. Therefore I needed to ensure the only variable used was "X". So I converted the equation in part 1 above from X=Y+8 to Y=X-8 and substituted (X-8) for Y in Part 2. The FInal equation is as follows: X+1 = 2(X-8+1) X+1 = 2(X -7) X+1 = 2X -14 X + 15 = 2X 15 = X (Beth's Age NOW)

[@beatrizcansado8080]

Yeah, I pretty much did the same. A system of equations, I find it to be the fastest way.

[@martm216]

Being creaky at maths I made heavy weather of this and set it out as a simultaneous equation. I called Beth's age b and her brother's age a. So: 1) b - a = 8 2) b +1 = 2(a + 1) b = 8 + a Substituting in equation 2: 8 + a + 1 = 2a +2 gives 7 = a or a = 7. So Beth's age is 15. It got me there but his way was shorter. (Once he got around to it!)

[@gerardjlaw]

Very wise! (That's how I originally did it, too.) Of course, setting out simultaneous equations is really just a different way of looking at the process of substituting for one variable with an expression in terms of the other, but I find it a particularly clean and satisfying way of laying out my working. (And it's easier to check over for errors when her age comes out as a minus number!)

[@martm216]

@@gerardjlaw thank you - yes I'm sure you are right. I was pleased when at the age of 32 or 33 I finally managed to do simultaneous equations, having been quite defeated by them at school! My maths teacher at school was one of those who was interested only in those bright sparks who picked it up quickly. Whereas the teacher at the evening class was patient and actually taught us.

[@gerardjlaw]

@@martm216 I know the type well. I taught maths at high school and didn't see eye to eye with many of my colleagues.

[@martm216]

@@gerardjlaw ah, interesting. Was this in America or Britain? My maths teacher was a nice old guy, but like I said interested only in his group of bright boys. The rest of us were left to flounder. He actually taught my old dad at the same school. Only in those days he was the physical education teacher. We had a mature student teacher come for a few weeks and he actually tried to teach us. I was starting to see the light a bit but then he was gone. But the teacher at the evening class was good. I've got quite high qualifications in English and Literature, but getting that GCSE maths was one of the proudest achievements of my life!

[@gerardjlaw]

@@martm216 Scotland. (Standard Grades and Highers rather than GCSEs and A-Levels.) I came to teaching later in life, and I was pretty unimpressed with most of the ones who'd been doing it since graduating.

[@Loveitmore1]

I mean no offense, and I love your content, but why is it that when every video has feedback about it being long winded, subsequent videos seem even more long winded? Math is tedious enough for most people to learn.

[@robertfrydell703]

21 minutes of my life that I'll never get back.

[@johnalanelson]

I solved this based on the thumbnail and watched the video to see if more data was supplied that would clarify which of the two possible answers was right, but no such data was supplied so there are two answers which are equally valid. It says she will be twice his age next year, which implies that she won't be this year, so this will be after her birthday next year. Since she is 8 years older than her brother, she will be 16 next year, but the question is *how old she is now* . What we don't know is if they have had their birthdays *this* year yet! Solution #1 (most obvious, but less likely) If we *assume* that that they have both already had their birthdays this year then Beth is 15 (and her brother is 7) Solution#2 (less obvious, but far more likely) If we assume that they have *not* yet had their birthdays this year, then Beth is *now* 14 (and her brother is 6). Since this was posted on Jan 12, it is far more likely than not that they have not yet had had their birthdays this year.

[@kc4cvh]

The question is a problem due to ambiguity: 'Next year' presumably, but not certainly, means a birthday for Beth has passed. This leaves the possibility that Beth's age is twice her brother's now if there be no birthday for her between the present and the undefined future date.

[@greenriver520]

There can be a what if in this one. If the question is asked in mid December, and the birthdays are not until June, the answer could be 16. She is 16 in December, while her brother is 8. If their birthdays are on the same day in June, she will still be 16 and twice as old as her brother in January, next year.

[@johnalanelson]

It says she *will be* twice his age next year, which implies she won't this year, but we don't know when. though it implies it will be after their birthdays. Since we don't know if they have had their birthdays this year, her age now could be either 15 or 14. Given that this was posted on Jan 12, it is far more likely that she is still 14!

[@kev7161]

I just made a table with 5 possible ages for the brother and added 8 to each one for Beth. Then I added 1 more for next year for the brother and multiplied by 2 for Beth until I found the answer (2X) in about a minute. Then returned to this year to get the answer of 15. But I know there was no algebraic equation, so I understand where he was going. It was just taking a long time.

[@greekguytalks]

he is questioning 10 year olds obviously but good job you get a cookie....

[@JimiBurleigh]

Had this sussed straight away. But the "method" of solving this sort of thing will be helpful for more complex problems.

[@krisainsworth239]

I really like your math videos but please cut down on the babble! You didn't even start looking at the problem until more than 5 min. in !

[@fishermanfrank4522]

Quite agree. Maths is dealing with figures not speech - cut the cackle and get on!

[@mjcard]

Knowing he does this I skip forward to the information I want to learn.

[@lamper2]

You can ALWAYS fast forward-some of us like his teaching style because he is teaching BASIC PRINCIPLES that apply to way more than just this specific problem.

[@rogercline5377]

She's eight years older than him, and she will *always* be eight years older than him. She'll be twice as old as him when she's twice...the amount older than him she is. Twice eight is 16. That's next year, so now she's 15 and he's 7.

[@gerardjlaw]

Presumably, then, she'll be three times as old as him when she's three times the amount older than him she is??? (Spoiler alert - she won't!)

[@rbwannasee]

Beth is always 8 years older than her brother, but will only be twice as old once. You can plot those as linear functions on a graph, then you're looking for the intercept. Algebraically this means solving for zero, substitute in other expressions you already know, then subtract one. Bazinga...

[@willowvons]

Took me just shy of 15 seconds to know the answer. Thank goodness I didn't have a teacher like this one!

[@tommyhunter1817]

Enjoyed this. I am a 51 year old civil engineer, so I’ve done A LOT of algebra. It really is the most useful math in life. You did an excellent job explaining--and believe me, I have heard a few people try.

[@tommyhunter1817]

@@davidbattaglia5187 try to teach our trade to a high school sophomore. GUARANTEE you’ll sound boring--or your students won’t have a damn clue what you did.

[@capers72424]

While I understand the importance of explaining things, this goes on and on and on and I lost interest. Due to someone else’s comments, I jumped ahead to 9:32. The table is, indeed, a very helpful device, but the whole thing can be explained in five minutes. One minute to drone on, one minute to set up the table and explain it, one minute to develop equations from the table, one minute to solve the equations, and one minute for a victory lap. I can’t imagine why this needs 21 minutes of droning!

[@johnalanelson]

And yet, he still misses the fact that there are two equally valid answers and his answer is most likely wrong!

[@capers72424]

@@johnalanelson oK. I will bite. What is the other answer that you feel is better, and how is his answer wrong? Did he come up with Beth being 15 now? I didn’t stick around for his conclusion.

[@johnalanelson]

@@capers72424 He came up with 15, but since it was Jan 12 and we don't know when her birthday is she is most likely still 14. The wording allows for two different answers and since she probably was born after Jan 12, she probably is still 14.

[@capers72424]

@@johnalanelson sure, OK. I can see that. Thank you.

[@juanitawatson596]

I'm so glad to I've met you! You are the best. Thank you.

[@pingan1006]

💌 Many thanks for your advice. I subscribed after watching this video ( The very first of your video ) . Besides teaching us how to solve this problem , you also teach us about attitudes to learning maths. Awesome and your teaching is step by step. Very very very clear. Many thanksss...... 🤗🤗🤗. You have a very nice day too 🍿🍟🥧🍫🍫☕.

[@saleemqubain4542]

Hi we really appreciate your auditorial forgive me to say that but you make it boring by repeating your self on every video (Sorry)

[@edwardd8751]

Yes very true.He wastes the first 10 minutes waffling on about nothing. Also why do they persist in calling maths math. It is short for mathematics and therefore should be called maths.

[@jackedwards7420]

Figured this out in less than a minute in my head, no algebra needed, just simple logic! She's 15!

[@bwghall1]

in one second I made 16.

[@ladamyre1]

​@@bwghall1 Next year she'll be 16. The question is 'how old is she now'.

[@gerardjlaw]

I presume you doubled eight to get sixteen? Why??? Granted, your answer matches the correct answer, but that's just a coincidence caused by the brother's age (the thing you SHOULD have multiplied by two) being the same as the age differential (the number you actually - but mistakenly - multiplied by two). Not convinced? Try it with Beth being THREE times her brother's age. Do I hear the words, "She'll be twenty-four." wafting this way? That IS what your reasoning demands, but it's wrong. In fact, she'll be twelve, as the algebra makes clear.

[@gerardjlaw]

@@bwghall1 In that case you made a catastrophic error. You may wish to read my analysis above.

[@gerardjlaw]

@@ladamyre1 His do you know she'll be sixteen? You didn't simply multiply eight by two, did you??? You may wish to read my analysis above.

[@DeanG55]

You are the best teacher!! I am recently retired and am enjoying learning math all over again!! LOL!!

[@Strappa71]

In the actual solving of the equation there is not really a need to take the long way around and making things negative. I prefer this way. x+9=2x+2 ; x+9-2 = 2x+2-2 ; x+7 = 2x ; x-x+7 = 2x-x ; 7 = x ; x = 7. No confusing negatives.

[@charliewyatt6997]

Wow, that makes it seem so complicated. All it’s asking is (8 x 2) -1. Got to be 15, and it takes seconds.

[@gerardjlaw]

You think so? Why did you multiply the age difference by two? The question didn't say that Beth would be twice the difference in their ages. Granted, your answer matches the correct answer, but that's just a coincidence caused by the brother's age (the thing you SHOULD have multiplied by two) being the same as the age differential (the number you actually - but mistakenly - multiplied by two). Not convinced? Try it with Beth being THREE times her brother's age. Do I hear the words, "She'll be twenty-four." wafting this way? That IS what your reasoning demands, but it's wrong. In fact, she'll be twelve, as the algebra makes clear.

[@charliewyatt6997]

@@gerardjlaw I just used common sense. Common sense dictates that if Beth will be twice as old next year and that there is an 8 year age difference, then next year she will be 16. Common sense also then means that if she is 16 next year, she must be 15 this year. It doesn’t matter when her birthday is during the year. She must still be one year older after the passing of one year from now. If the maths problem had dictated that Beth was 3 times her brother’s age, then the method of calculation would have been different.

[@gerardjlaw]

@@charliewyatt6997 One problem with "common sense" is that its lack of formal logic can lead to undetected errors. Another is that's no use in tasks like computer programming, where the machine doesn't have any "common sense" and can only carry out precise instructions. The aim of Zimmerman's video was to help people to understand how they could express a problem presented in everyday language in a formal mathematical form and then derive the correct answer, no matter what numerical relationships had been specified.

[@charliewyatt6997]

@@gerardjlaw luckily I’m not a computer.

[@gerardjlaw]

@@charliewyatt6997 I was pointing out that "common sense" wouldn't help you if you wanted to program a computer.

[@TrulyMeli]

This guy was taught to waste time. He needs to start explaining these in 10 min or less.

[@cdmcintyre1854]

Did this in my head in about 8 seconds with simple logic and common sense. This guy rambles on and on for a LONG explanation.

[@michaellee891]

I believe his method is purposeful for those he's targeting. Individuals struggling with problems like this tend to get anxious. Anxiety will lock your brain in a death-grip, not allowing you to reason and comprehend normally. IMHO, his is manner has a calming effect and helps relieve stress. If one is stuck with the feeling of: 'I can't do this'! He can help. Notwithstanding, you can always FF to get to basic problem, you just have to get out of the box.

[@greywebb1472]

Way too much talk. Get to it. I don’t have all day!

[@phillipnicholson187]

You are to long winded

[@fishermanfrank4522]

You are soooo right!

[@MrMousley]

Questions like this are actually my favourite type of maths question !! The brother is X and Beth is X + 8 NOW So next year the brother will be X + 1 and Beth will be X + 9 and X + 9 will be twice X + 1 .... 2(X + 1) = X + 9 2X + 2 = X + 9 Subtract X from both sides X + 2 = 9 Subtract 2 from boh sides X = 7 BROTHER is 7 and BETH is 15 .... and next year 8 will be half of 16

[@chris_palmer_sr]

I had this when I read the 'thumb' and I have loathed even the word 'algebra' for over 50 years. That, imho, is what they called 'critical thinking' before .. I learned more about algebra reading comments in a few minutes than I did during 2 years of 'algebra'. (in fairness, I was 1A and had more interest in a certain cheerleader's uniform that sat next to me, both years. Vietnam was raging. No one even asked what I was doing after High School - it was a done deal.) .. thank you.

[@sbpierce9987]

Nothing but gab for over 5 minutes, folks. Fast forward.

[@arthurclifford8290]

If showing the table, I think it would help to understand how to identify an equation to show that if you add another row with "Age Next Year" also in the first cell and Beth's age as 2(x + 1); because you have two rows that represent the same thing (have the same value in the first column), if there are values in the same column for the equal rows they can be shown as an equation. Age Next Year.Beth1 =Age Next Year.Beth2 => x+8+1 = 2(x+1). Then of course you solve for x (x=7), then plug in the result into to x for the formula in the cell that answers the actual question (Age Now.Beth = x+8): 7+8=15.

[@charlesward8196]

I got to X + 9 = 2X+2, subtracted X from both sides, and subtracted 2 from both sides, and got to X = 7, without messing around with negative numbers. Then X + 8 = 15, Beth’s present age.

[@arlliegreen7555]

Thanks John, love your teaching method. ❤

[@aussiefox2000]

I loved this one. I got it in under 30secs. Never did get one of your other vids though 🤣🤣

[@excellentlistner5925]

I am excited to discover your videos. I was a horrible student. Graduated college with a BBA and the minimum GPA, just enough to get out. Now 66 years old after a long career in business I want to learn. After reading the problem one time I knew Beth was 15, brother is 7 but lost you in at about the 10 minute mark in the video. Got to the end and never saw the answer, had to scroll back to discover the Brother is 7. Sorry I was confused. I will keep trying

[@hitechburg]

My math teachers made algebra, geometry and trigonometry FUN. I would have learned nothing with this guy!

[@3bdallahs263]

You are the best! thank you sir.

[@goillini1271]

Why are people criticizing him? My 8th grade Algebra teacher told us she didn’t want to teach word problems … it took me until college to have a competent teacher. This is great! Kudos to him!

[@vlsui66]

Bc he takes wayy too long to explain the answer to this example problem. If you want an in depth explanation, he should have done a general video on that separately and this video should be short and sweet, showing the steps. But he instead takes 25 minutes just to solve a mere example. An example.

[@markdupont1080]

Thank You! Well Spoken!😁

[@Maninawig]

Though this is a year old, I am excited to learn from my mistake on your latest video and see if I can solve this one: Let's use x to represent Beth and y to represent her brother. The first sentance would state y=x-8 while the second would be 2(y+1)=(x+1) 2y+2=x+1 2y=x-1 2(x-8)=x-1 2x-16=x-1 (gather the x) 2x-x-16=-1 x-16+16=-1+16 x=15 Beth is 15 making her brother 7

[@xavierkreiss8394]

"If you're not going to do maths the right way, don't do it at all". I totally agree, and so would many other people like me. But unfortunately in school we had no choice, we were forced to do maths, it was part of the syllabus. So we did maths but did it wrong. I got to university and dropped maths altogether. I've avoided he subject all through my career.

[@robertvarisco2196]

I came to the same result in what seemed like a simpler way. I began by writing two equations: If B represents Beth's age and A represents her brothers age, B=A+8 and B+1=2(A+1) Starting with the second equation, B+1=2(A+1) B+1=2A+2 B=2A+1 Now referencing the first equation, substitute A+8 for B. A+8=2A+1 A+7=2A A+7=A+A Subtracting A from both sides of the equation gives you 7=A Since B=A+8 and A=7, then Beth is 15 and her brother is 7.

[@raulmichel7630]

Thank you. It did help.

[@v-gc7257]

Always had a tough time with this; Time to review

[@nj-1008]

I was able to simply figure this out in my head within a minute. LOL

[@joannejennings7649]

Sure helped me. Thanks

[@chessmentor63]

Took me all of three seconds to determine in my head that Beth is 15 now. Then again I learned algebra a half century ago.

[@clairgarrick9842]

As a former math teacher, if I talked this much without getting to the problem, my students would be like RIP Van Winkle

[@MrBobbybrown7]

I solved this problem with a slightly different approach initially , using 2 variables ( one for Beth’s age and one for her brother’s age) and 2 equations. I then solved both equations for one of the variables. Since both equations are now equal to the same variable they are equal to each other. I used this to create a new equation with 1 variable now and solved it. I like your approach more however since it seems more systematic and involves only 1 variable. However the problem could’ve been solved intuitively (I didn’t think of this until after I’d solved it!) by realizing that since the siblings are ALWAY 8 years apart and next year Beth will be twice as old as her brother we can reason: (2*8)-1= 15 which must be Beth’s age currently. The moral is always try intuition first! Big fan of your content!

[@tyronekim3506]

Wrong. Getting the answer by intuition is a crapshoot - sometimes it works and times it's a failure. This is especially true when problems are non-linear.

[@MrBobbybrown7]

I actually agree with you to a point. What I was getting at had more to do with the evolution of mathematical thought which was fostered largely by scientific discovery. Ancient math was almost exclusively pattern recognition and exploitation. Pythagoras, Euclid and Muhammad ibn Musa al-Kwarizimi lived at a time when there was little need for abstract calculations but there was ample need for more practical issues like area and distance which are geometric (or pattern based, if you will) math disciplines. Pythagoras’ most famous theory was developed completely in intuitive environment, for example. Joy of X by Steven Strogatz really does a great job explaining the intuitive nature of math, but yes, there are lots of times when methodical calculations are required.

[@spiderbloke1075]

She is the same age as Jane. I know this because Jane is in my class and she told me so. Jane is very honest .. ty

[@johnspence8141]

Next year, B+1 = 2 (x + 1) as well. Or B= 2x + 1, therefore 2x + 1 = x + 8, x=7

[@tommybaker4330]

How do you show your work when you do it in your head like Mr Owens and I did?

[@capnbobretired]

Yes my first job on my license the captain asked me to solve this very problem. Oh wait, no he asked me to calculate tide height at sailing, time of moon rise after sailing, the light signals on the light houses we would expect to see after leaving Baltimore until sunrise, and to get a crew check done. Real tasks for a real life.