The cost of your favorite tea doubled, with 7% tax you now pay $12.50, what was the original price?

How to solve an algebra word problem about percent and price.
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[@kennethdias9988]

5.84 12.50 divided by 1.07 =11.68/2 = 5.84 Easier to pull off the tax and divide by 2.

[@slshusker]

That is the way smart people figure out the word problem.

[@inyobill]

@@slshusker Ahhhhh, compliments. I worked in software. hard to understand, convoluted code is easier to create than simple, easy to understand.

[@slshusker]

@inyobill , After taking unrequired advanced calculus and other math in high school I knew I wouldn't really need to use it much in the future, yet here I am suckered into math videos.

[@user-hj8bo1dz6o]

This problem has an issue with semantics. There is a distinct difference between "cost" and "price" as the problem is presented. The price includes tax; the cost is before tax. The problem asks for the original sell price, not the original cost. The answer provided of $5.84 is the original cost. The problem indicates that a 7% tax applies. If tax is added to the $5.84 cost, the original sell price would be $6.25. Probably doesn't matter though, as this business will not survive; they do not appear to have any profit built into their price.

[@waynestanley01]

The price is how it is advertised on the shelf (before the tax) in layman's terms that is also the cost but the tax is an additional cost add together to find out what you have to pay. Go to a car dealer and you will see a price on the windshield but it will cost you a lot more when all the fees are added.

[@Truth845]

🤣🤣🤣

[@devonwilson5776]

Greetings. The original price is $5.84. We determine the original cost as follows. First, it is assumed that the original cost is $X. Now, if we double the original price, we will get 2X dollars. Thereafter, we add 7% taxes to get 2X times 7% for the tax amount added. We will now equate double original cost plus the added taxes with the total, $12.50, paid. That is 2X+14X/100=$12.50, and 200X+14X=$1250.00, 214X=$1,250.00, X=$1,250.00/214 and X= $5.84, original cost. Proof. Twice the original cost is $5.84× 2=$11.68 7% taxes of the price doubled is $0.82. If we add twice the original cost and the taxes we should get $12.50, and we do. $11.68 +0.82= $12.50. Lovely.

[@patriciamillin1977]

Okay. I solved it differently: $12.50/107x100 = 11.68/2 = 5.84 I guess algebra just wasn’t in my head when I read the question, lol

[@63SpaceGirl]

I've always done math different 🤣 12.50/1.07 to get current price less 7% tax, then divide by 2 to get original price 🎉

[@inyobill]

@@63SpaceGirl Hence, I can interpret "differently" as simple and straight-forward. It's amazing to me how convoluted these simple calculations can be presented.

[@devonwilson5776]

@@63SpaceGirl Greetings. Hm! Brilliant. That is absolutely brilliant. I totally did not see it that way. However, I absolutely follow your line of reasoning. Your method is clear for me to understand. The total price paid, $12.50 divided by 1.07, the cost doubled plus the 7% added, equals, $11.68, the cost/price doubled. Now, all that is left to be done is to divide that price by 2 to get the original price or cost for which the coffee would have been offered. Blessings.

[@Mark_Lacey]

Once again, your English vocab is letting you down (maths teachers meh!). The question should be "what was the original price excluding 7% sales tax?" I know you say this in the video but many of us just go off the question on screen before watching the video. I went with (x) . (2) . (1.07) = 12.50 x = 12.50 / 2 / 1.07 x = 5.84

[@jameshicks3453]

12.54 divided by 1.07 equals 11.68. Half of that is 5.84

[@lp1330]

Exactly no need to stretch it out to a 10 minute production

[@asphaltandtacos]

My approach is 1.07x = $12.50 with the result divided by two. Sometimes breaking down the problem into smaller parts is a better way to find the solution.

[@justpinkcandy]

So easy. put a 1 in front of the decimal place of the percentage (7% = .07), so 1.07. Divide total 12.50 by 1.07 = 11.68 ÷ 2 = 5.84

[@AbaYHUHisKing]

I find it ridiculous how they want to confuse you with all the formulas by model. Just get straight to it...and be done with. Easy breezy.

[@davidfoster3427]

nothing I threw it into the harbour

[@steveswoodworking2504]

Easy to figure out, although my answer was different than yours. If it is $12.50 with tax, then I think the answer is 6.25 was the price before - with tax. But yes, the 5.84 before tax was super easy to come up with, without watching the video. (12.50/1.07)/2

[@laurendoe168]

I did it the long way, removing tax, cutting in half, re-adding tax... only to come to the obvious conclusion... the tax would ALSO have been half!!

[@patriciamillin1977]

I calculated it completely differently, not using algebra, but came up with 5.84. Only I then mad the mistake of adding 7% again (because where I live it’s always 7%) and also came up with 6.25. That totally confused me.

[@davidarmitage677]

I agree, I thought it should be 6.25, but thought that there must be more to it than that.

[@marymaryquitecontrary]

The question was "the original price," not "original price with tax." We don't even know if there WAS 7% tax on the original price.

[@GFlCh]

The final answer is closer to exact than you think... If the tax (on 11.68) is 0.8176, then you would pay 0.82 tax, and the total would be 11.68 + 0.82 = 12.50.

[@TheSimCaptain]

The question didn't explain if the same tax was in place for the OP, and whether the original price incuded the tax. Very confusing.

[@throngcleaver]

I did it this way: 2X(1.07) = 12.50

[@danieldennis9831]

Original price was $5.84, and you paid $6.25 with tax. The price doubled to $11.68 and you now pay $12.50 for the same tea. p=original price n=new price n•1.07=12.50 n=2p n=11.68 11.68=2p 5.84=p Original price was $5.84.

[@danieldennis9831]

I will say that it isn't approximate. $5.84 was the original price. It just so happens that the amount you pay is approximately 7 percent higher than the cost. But it is often rounded to the closest penny.

[@melonhead3649]

Answer different depending which country you're in, affects how you read the question, I think

[@colleencurrier1586]

$6.25 plus .07 tax

[@pqsk]

Good one. I caught the *doubled* but then the tax threw me off and I forgot lol

[@phrankus2009]

If The Boston Tea-Party is taken into consideration, I would guess, "TOO MUCH!"

[@MrMousley]

I hope that I am understanding the question properly and that you are saying .. $12-50 = twice the original price + 7% of twice the original price 2P + 7% of 2P = 12.50 express the % as a decimal 2P + 0.7 x 2P = 12.50 do the multiplication 2P + 0.14P = 12.50 do the addition 2.14P = 12.50 divide both sides by 2.14 P = 12.50 / 2.14 get the calculator out ! P = 5.84 to two decimal places Original price = $ 5-84

[@geniferteal4178]

Interesting way to look at it.if the price doubles the tax effectively doubles compared to the original. You then solve for the final number in one calculation. Kind of like the Rubik's cube. There's lots of ways to solve it. you just did it in the fewer moves.

[@paulpurpura191]

Let’s red-do the Boston Tea Party again.

[@russelllomando8460]

good one

[@lowlightevangelist9431]

Can tell this professor has successfully dealt with a bunch of smart mouthed brats. Glad he hasn't lost the joy to teach!

[@keithschipiour4684]

I dont know will ask HR block when they do my taxes.

[@carolleenkelmann3829]

Who thought of the moving of the two points when dividing by a hundred in %. ?

[@user-dd2jf4cb6j]

What app do you use for drawing thus?

[@user-vo4ze2dd6e]

12.50/1.07/2=5.84

[@SirPhilosopher]

My problem with word problems is more grammar than math. It’s unclear if a 7% tax doubles the cost of the tea or a 7% on top of the doubling. Does it matter what the tax rate was before? And it’s ambiguous if the original price was with or without tax. I’m not picking on your problem. It’s the converting one kind of language to another. Not a knock on the video. Just triggered an old gripe.

[@carolleenkelmann3829]

Don't worry about the maths. I AIN'T BUYING NO TEA AT THAT PRICE! ( 100 gms). That's the same price as those predigested coffee seeds! - the most expensive in the world.

[@Kyrelel]

You should make it clear whether the total cost has doubled, or just the price of the drink has doubled.

[@kimbybean001]

Your question was not clear. The original price with the lower tax? The original price before tax and before the increase in tax, the original price after the increase in tax but before applying the new tax and if it's before the increase in tax, how are we to know what the original tax rate was, before it was increased. Is there a way to calculate that? I had to play back 2:33 at 0.5 speed, to TRY to understand the words were you saying. "Math.....X.......X......." Still, it was not easy to understand "word problem". Anyway, I think I am too analytical to be watching such videos. I do enjoy them though.

[@dunesunny3131]

The question/ problem does not state how much tax was on the tea before. So what was the % of tax paid before?

[@derekwinston4105]

Sales tax is a set rate irregardless the price of the item. Therefore 7% of the original price + the original price = 12.50 or in math .07x + x = 12.50 where original price is equal to x so x = 12.5/1.07 then divide this number by 2 to get the original price.

[@kennethwright870]

(12.5/1.07)/2

[@ldewproductions7271]

Half $12.50 is $6.25 that's the answer.

[@sandblek6974]

What does tax have to do with it? If I pay $12.50 and the price has doubled, it obviously was $6.25 before that. As a customer, why should I care about tax, I only care about what I really have to pay in the end, regardless of the tax.

[@waynestanley01]

Stores advertise prices before tax

[@user-ri6rn7ti5h]

= 17:60

[@martinfiedler4317]

In this case, the difference is small, but strictly speaking the result depends on if a) the tax is applied on the pre-tax price of the tea, or b) the tax is a fraction of the tax-included sales price For "a", the old price is p = 12.50 / 2.14 = 5.8411.... For "b" it is p = 12.50 * (0.93 / 2) = 5.8125 So, you need to know how exactly the tax works

[@inyobill]

Each unit is doubled in price, the price is not for two units. The new unit price is 2 * 5.84 = 11.68. round(1.07 * 11.68, 2) = 12.50. No ambiguity.

[@martinfiedler4317]

@@inyobill Sales price is 12.50 After-tax price is 12.50 * (1 - 0.07) = 11.625 Old price is then 11.625 / 2 = 5.8125 Yes, you need to be sure about how the tax is actually levied. Otherwise, you have to clarify the assumption.

[@Truth845]

Thank you for clearing that up. My answer was $5.81😊

[@williamniver6063]

Martin, I hear what you are saying, but you are, in part, confused, and I think I see how. Only your first scenario (a) makes any sense in the real world. OF COURSE, tax is computed on the "pre-tax price" of a good - where else? Your second scenario (b) is in error because your equation 0.93 x $12.50 does NOT yield the original price of two widgets plus 7% tax; it only tells us what 7% of the grand total, out-the-door cost. Using 0.93 as a multiplier is wrong. As others have pointed out, you must instead divide the total cost (original cost plus sales tax) by 1.07 in order to arrive at the original cost of two widgets. MULTIPLYING BY 0.93 IS NOT THE SAME AS DIVIDING BY 1.07. q (1+t) ≠ q/(1-t) Lather, rinse, repeat.

[@williamniver6063]

​@@Truth845Martin did NOTHING to clear anything up. He is quite simply wrong. See my comment below. q (1 + t) ≠ q /(1 - t)

[@kamilshere9186]

😂6,25 dollars

[@muchomacho2504]

Everyone has an easier solution; the video is overwrought. A much simpler approach is to cut the given cost in half to obtain $6.25 and remove the tax dividing this number by 1.07. Done!

[@bobcornwell403]

I ended up with $ 6.25.

[@michaelparker4952]

$5.84, I got it!

[@Vipre-]

About $5.84

[@LizzieWhiz]

I HATE algebra, my dyslexic brain screams NO...does not compute, what is this sheet! Why are letters used when numbers are perfect. Now I understand algebra's use in coordinates but for a simple Maths problem I don't get it. This is how I worked it out and you said at the end approximately which is not exact. 7% X 12.50 =.87.5. 12.50 - .87.5 =11.625 X.5 = 5.8125....am I wrong? I will keep watching your videos because I enjoy them and I have told my friend to come watch them because they might be able to help their teenage children.

[@jebbiekanfer8843]

5.83 rounded off

[@jebbiekanfer8843]

Down

[@deograciousuwiragiye8429]

11.6$

[@FlyingGemSparkly]

$11.62

[@geniferteal4178]

Poorly worded how could a 7% tax double the cost of an item?

[@waynestanley01]

he should have said the price doubled

[@geniferteal4178]

@waynestanley01 I get what was meant I just initially read it wrong. Subtract the 7% tax then cut the number 1/2. if all else fails throw the tea overboard! LOL.

[@derekwinston4105]

X = price before taxes .07x + x = 12.5/2 Solve for x

[@user-ed4xc7fl2y]

11.65

[@tomtke7351]

very well stated problem. The task is to first convert words to equation format... then solve it. $12.50= (1+0.07)(2×O) where O is original price.

[@govindangandhi9600]

Good morning. your video mixes price and cost. the cost of your favorite tea has doubled and with 7% tax, it is now 12.50. the calculation yields the original cost and it is correct $5.84. but you wanted original price. original cost includes 7% tax so you have to calculate the new amount for the price which $5.46.. Thanks for reading.

[@waynestanley01]

I think the words price and cost are interchangeable You could as someone how much does this cost or you could ask them what is the price. When you add the tax then it's how much do you have to pay and or it is an additional cost.

[@waynestanley01]

Price would have been a better word to use

[@williamniver6063]

Except you are wrong. True, cost does NOT equal price (WayneStanley is mistaken); price is merely the selling point, the agreed upon value of something, but cost refers to the total outlay for a purchase, and might include, as here, taxes, fees, offsets, other components to the out-the-door amount. But you get confused yourself when back-thinking this problem and end up taxing the widget TWICE, which isn't implied by the question or logical in the real world. Try your answer, see if it satisfies the problem. If one widget is $5.46 but doubles in price, the new price is $10.92. The sales tax would be 7% of $10.92, or $0.77, for a total cost $11.69, not $12.50. Hmmm.... But wait a damn minute! If we arbitrarily tax the thing AGAIN, let's see what happens. Ok, here goes.... 7% of $11.69 is $0.81... so added together... $11.69 + $0.81... I'll be damned! It totals $12.50! ALL WE HAD TO DO WAS MISUNDERSTAND THE QUESTION AND THROW IN A MYSTERIOUS SECOND SALES TAX EVENT. Of course the answer - the only answer - is $5.84.

[@williamniver6063]

​@@waynestanley01 "Price" denotes a selling (or asking) point, an amount agreed upon by buyer and seller. "Cost", however, refers to the total outlay regarding a purchase, so it is comprised of the selling price plus taxes, fees, offsets, levies, etc Your cost is almost always greater than the price. If you sell your house, your gain (or loss) will be reduced by the amount of the real estate agent's fees. If you buy.a car, your cost includes the sales tax you pay to the state. The fees you pay your agent are negotiable, and don't affect the selling price of the house, nor does your state"s sales tax change the price of your car. These fees change your cost, not the item's price. The terms are neither interchangeable nor synonymous.

[@govindangandhi9600]

@@williamniver6063 you are correct

[@user-ri6rn7ti5h]

12.50+0.7= 12:57

[@RobiBue]

Just curious, could you explain your thoughts behind this approach?

[@Eewec]

Hmm interesting phrasing. If the cost of my favourite tea doubled then the amount of tax is irrelevant. The cost to me is the money I pay, if that doubled then the original price is half what I pay now. *if* you mean, the net cost of the tea (without tax) doubled instead of the gross cost (including Tax) then you need to state that. Classic culture clash type stuff. In America the tax is not included when you look at the cost of something on the shelf of a shop, pretty much everywhere else, if it's priced at £5 or €5 on the shelf then that's how much you pay. The Americans will give excuses as to why this is, but they all basically boil down to ripping off the consumer. Oddly, they're the only country with such a backwards system. Also; $12.50 inc Tax for the Tea now $12.50/1.07=~$11.68 without tax for the Tea now ~$11.68/2=~$5.84 without tax for the Tea before ~$5.84*1.07=$6.25 with tax for the tea before So... the old price is exactly half of the current price of $12.50 Even if the tax is levied as 7% of the final sale price it's irrelevant; $12.50 inc Tax for the Tea now $12.50*(1-0.07)=$12.50*0.93=~$11.63 ( actually 11.625 ) without tax for the Tea now ~$11.63/2=~$5.82 ( 11.625/2 = 5.8125 ) without tax for the Tea before ~$5.82/0.93=$6.25 ( 5.8125/0.93 = 6.25 ) with tax for the tea before (Edited due to getting my operations mixed up) Either way I would have paid $6.25 at the checkout for the tea before it doubled in price. So... yeah... why go the long way round when you only need to divide by 2. EDIT:; About the only time it's worth doing this the long way is if both the pre-tax cost and the tax rate both changed at the same time and you're trying to work out if the government or the shop is trying to scalp you... the answer is probably yes.

[@portionsredacted7743]

@TabletClass $5.46 before tax Mr. KZbin Math Man, This is what we used to call a bad Scan-Tron question, back when we filled in the answers on electronic Scan-Tron forms. The problem doesn’t take into account that the original price would almost certainly have been taxed as well. So your answer of $5.84 should be 107% of the original price, not the op itself. Therefore, if x represents the op, 1.07x = 5.84 x = (5.84)/(1.07) x = 5.46 (rounded) Original price of tea, before tax, is $5.46

[@ve3mzo]

i got $5.81 $12.50x.93/2=$5.81

[@generalgrafx]

Think of $ 12.50 as 107%, so to get the amount before tax- 100% - you have to divide 12.50 by 1.07, which is 11.68. Divide this by 2 and you have the original price of the tea ($ 5.84).

[@ve3mzo]

@@generalgrafx figure this way 12.50 100% with the tax in remove the 7% leaves you with 93% so .93 x 12.50=11.625/2=$5.81 yes no that's the way i interpret the question ??

[@waynestanley01]

you are removing 7% from the final number(0.875) which is more than the 7% of the principal(0.8176) @@ve3mzo

[@ve3mzo]

@@generalgrafx how the question was asked it could be interpreted in both ways , i look at it with the 7% added in making it 12.50 100% , you look at it by adding 7% to 12.50 107% i think the question was poorly asked ??????????? in canada both would be correct the smallest currency is 5 cents making it $5.85

[@bc24roxy4]

$5.81? 12.50 - 7% tax =11.62 ÷ 2 Ill watch now and figure out why im 3 cents off

[@generalgrafx]

The 7% tax was added to $ 11.6822, which results in 12.50. You cannot just subtract 7% from 12.50 to go back to 11.6822. Why? because 7% of 11.6822 (0.8177) is not the same as 7% of 12.50 (0,875). The right percentage to subtract is 6.54. -100*(11.6822/12.50)+100=6.54% 11.6822/12.50 = 0.9345, which tells you that 11.68 is 93,45% of 12.50 12.50/11.6822 = 1,0702, which tells you that 12.50 is 107% of 11.68

[@RobiBue]

When calculating percentages I always set up a visual equation to see what I have and what I want. In this situation, I know that 100% is the value of the double costing tea to which I will have to add the 7% to get the final price of 12.50. So 100% plus 7% equals 107% Therefore my visual equation looks as follows: 12.50 107 --- = -- 2X 100 Now all I need to do is solve for X Flipping the divisors (or cross multiplying) will bring the X to the top where I want it. 12.50 * 100 ------ = X 2 * 107 X is the original price before doubling 😉

[@user-dd2jf4cb6j]

This

[@WKUHilltopper]

Why do you make this a complicated process? I solved it with two simple calculations. No wonder kids hate math and fear it. Is this the "new" math? What BS!

[@michaelperine2333]

Math teacher flunks English again. Replace the comma after "doubled" with a period and capitalize "with". Alternatively, change the comma to a semicolon to show that there are two closely related sentences. Finally, the word "cost" is ambiguous. The definition of "cost" is the price of something that must be paid to acquire it. To make the question clear, you must specify whether cost includes tax. As the question posed, $6.25 may be the correct answer.

[@chadrew6]

$5.84

[@vibrantnubian27]

I got $5.81, why am I 3 cents off???

[@generalgrafx]

Probably because you subtracted 7% from 12.50. The 7% tax was added to $ 11.6822, which results in 12.50. You cannot just subtract 7% from 12.50 to go back to 11.6822. Why? because 7% of 11.6822 (0.8177) is not the same as 7% of 12.50 (0,875). The right percentage to subtract is 6.54.

[@waynestanley01]

to get back to the original number before a tax has been added, divide by 1 plus the fraction of the percentage (1.07), not take off 7 percent (multiply 0.93)