Ed has 126 bills, made up of $5s and $10s. The total value is $840. How many $5s does Ed have?

[@Hugebear222]

You did it again John. 55 yrs ago I was good at this, Now i'm encouraged to start all over again and not let age get in my way. You do great work sir, keep it coming.

[@devonwilson5776]

Greetings. The answers are 84, $5.00; and 42, $10.00 bills. We will assume that X represents $5.00 and Y represents $10.00. Now, the total number of bills added together equals 126. That is X+Y=126, equation 1. Further, we are told that the total number of $5.00 bills added to the total number of $10.00 bills aggregate to $840.00. That is, 5X +10Y= 840, equation 2. Moving forward, we have 2 equations containing the variables X and Y. We will eliminate one of the variables and thereafter solve for the other. Using the equations above, we will eliminate X by multiplying equation 1 by 5 and subtracting it from equation 2 to get 5Y= 210. Solving for Y gives Y=42. Now, we will substitute this value of Y in equation 1 to get X+42=126, and X=126-42=84. From our determination, the number of $5.00 is 84 and the number of $10.00 is 42. Solved.

[@Kleermaker1000]

We can also say: let X = the number of 10 dollar bills, then 126 - X = the number of 5 dollar bills. Given the info that the total amount is 840 dollars then 10X + 5(126 - X) = 840 dollars = 10X + 630 - 5X = 840 dollars => 5X = 210 dollars => X (the number of 10 dollar bills) = 210 : 5 = 42. So 42 bills of 10 dollar = 420 dollars and 840 dollars - 420 dollars = 420 dollars : 5 = 84 (the number of 5 dollar bills). And also: the total number of bills is 126, so 126 bills - 42 ten dollar bills = 84 5 dollar bills. But I prefer the method with two equations with X and Y.

[@random_precision_software]

OMG it took you until 8 and a half minutes before you even started to explain the answer 😮

[@mrdave507]

I like your videos, but you start explaining, and then you stop to talk about something, and then you get back to explaining and then you stop again. It's a little frustrating. But thank you.

[@Kleermaker1000]

LOL! Bob has the same amount of money and the same kind of dollar bills. :)

[@gelvinlane6097]

I did 10 (ten dollar bills) into 840 (total value) = 84 (tens). That takes care of the tens. Then, 126 (total bills) - 84 (tens) =42. So, that leaves 42 bills. But they're tens! Double that, and you have 84 bills. 84 fives. Sitting here having a beer and doing remedial arithmetic and I'm so happy I finally understand it :). LOL someday I'll be able to translate this into an equation.

[@25113732]

I love your videos, very educational... but the in-between straying from the actual solving to do a little rambling is frustrating, 😇 that dear sir, should be done as a conclusion after the process of the solution. Much 💕 keep doing this job. wonderful job

[@DarekKoczwara]

I just divided 126/3. It comes to 42. 42 ×$10 +84 x $5= $840 It makes no sense but it worked.

[@freeguy77]

It does make sense if you split the total amount equally in half for each denomination, as ONE answer would be for the $840. If you had a DIFFERENT number of total bills (instead of 126), you could solve it for a minimum number of bills, providing you had at least ONE of each. So, with 2 $5s (worth $10; since you can't work the problem with only an odd number of $5s, so it has to be at least 2 of them), the remaining $840 would obviously take 83 $10s ($830), for a minimum of 85 bills instead of 126!

[@raynewport9395]

We have no idea, but he sure has racked up some debts.

[@michaelbaughman8524]

I got off on the two variables tangent and had x + y = 126 and 5x +10y = 840 but didn't know quite where to go from there except trial and error, so it took me a couple of minutes. Good one!

[@ab_ab_c]

From the problem we can construct the following 2 equations: 1. some # of 5s + some # of 10s = 126 bills so: f + t = 126 or t = 126 - f (when solved for the unknown number of tens, which we will need below) 2. 5n + 10n` = 840 (Note: n` just indicates a different variable that represents the unknown number of tens.). So, the equation means, 5 * some unknown number of 5s + 10 * some unknown number of 10s = 840 Since we solved for t above (i.e. the unknown number to tens), we know that we can substitute 126 - f into equation 2 as follows: 5n + 10(126 - n) = 840 (note: we change the f to n, because is it the unknown number of fives, just as n in 5n represents the unknown number of fives) Then we solve for n using algebra as follows: 5n + 1260 - 10n = 840 -5n = 840 - 1260 -5n = -420 n = 84 (this means that there are 84 fives) Then we use equation 1 to determine the number of tens as follows: t = 126 - 84 t = 42 (this means that there are 42 tens) Then we check our answers to ensure they are correct using equation 2 as follows: 5(84) + 10(42) = 840 420 + 420 = 840 840 = 840 (this is true, so we know our answers are correct) Then we answer the problem question: "How many $5s does Ed have?" Ed has 84 fives.

[@alexredmonjr]

84 fives and 42 tens Since 126 $5 bills is $630, that leaves $210 unaccounted for. I took 210/5, which is 42 tens Subtract from 126, which gives me 84 fives.

[@ab_ab_c]

210/5 = 42 'fives', not 'tens'

[@michaelbaughman8524]

@@ab_ab_c Nope, Alex is right, 42 tens, not fives. Why? Because he is $210 short. Divide the shortfall into 5$ increments and you have the number of fives that need to be increased by five, that is, the number that have to be $10 bills instead of five.

[@ab_ab_c]

@@michaelbaughman8524 42 tens is correct, but not for the reason that you stated, because 210/5 means: how many times does 5 go into 210, which is 42. A better way to solve the problem is to take 840/5=168. Since 168>126 bills, we know that we need to convert some number of those fives into tens, hence: 168-126=42 bills. 42*10 = 420. 840-420=420. 420/5=84. Hence, we see that we need 42 tens & 84 fives.

[@loveoneanother1226]

Great explanation. Thank you!!

[@H_3_4_R_T_S]

Hello sir how are you? Could you please make a video about constructive response essay for CST MATH? Thank you

[@RyguyAB]

I don't understand how systems of equation is more complicated. 2 equations 2 unknowns. It's about as simple as it can get. Let x= number of $5 bills Let y= number of $10 bills Equation 1: x+y=126 Isolate a variable: x=126-y : this is now Equation 2 Equation 3: 5x+10y=840 (Because the total amount of money represented by x fives and y tens has to add up to $840 and so we need to multiply number of each bill by its value and add them together to get the total amount of money.) Isolate a variable again: 5x=840-10y x=168-2y: this is now Equation 4 Since we now have two expressions equal to x (from equation 2 and equation 4) we can combine them: x=126-y and x=168-2y So 126-y=168-2y Add 2y to and subtract 126 from both sides: y=42 But y is the number of tens so to figure out the number of fives we substitute y=5 back into equation 2 and solve x=126-42=84. So there are 84 fives. I wrote this out in way more detail than I actually did on paper. I could have solved for x directly, but I wanted to work on whole numbers so I chose to solve for y first.

[@Kleermaker1000]

But you came up with 4 equations, whereas two equations with x and y (the two unknowns) is sufficient. :)

[@bobcornwell403]

Ed has 84 $5 dollar bills. I'm going to watch this anyway to learn a more efficient way to solve this. I solved it in four steps.

[@alextrebek8293]

I prefer my way. Writing 2 equations and 2 unknowns (x and y). Then you put y in terms of x and substitute that for y in the other equation

[@MrMousley]

I just made the HUGE assumption that there were twice as many $5 bills than there were $10 bills .. which meant that if there were 126 bills in total that meant 126/3 = 42 42 $10 bills and 84 $ 5 bills and, surprise surprise, that gave me $420 + $420 = $840 !!!

[@freeguy77]

If the amount of $840 was split equally between the $5s and $10s, then that would be ONE answer! There could be other combinations of $5s and $10s that would also add up to $840, but a different number of $5s and $10s, but this one said it had to be 126 total bills, so the 84 $5s and 42 $10s, each worth $420, one-half of the total for each denomination.

[@jerry2357]

84 fives, done in my head. I started by checking that the problem made sense. 5*126=630 (done by using 126/2=120/2+6/2=60+3=63) and 10*126=1260. As 630

[@ab_ab_c]

That ^^ method is way too complicated. It is easier to take 840/5=168. Since 168>126 bills, we know that we need to convert some number of those fives into tens, hence: 168-126=42 bills. 42*10 = 420. 840-420=420. 420/5=84. Hence, we see that we need 42 tens & 84 fives.

[@richardowens9061]

@@ab_ab_c That is exactly how I did it in my head.

[@davidhandyman7571]

I worked out the answer before starting the video. Let x = the number of fives, and y = the number of tens. Then 5x + 19y = 840, and x + y = 126. As there are two fives in a ten, the number of 5 units is 840 divided by 5 = 168. Therefore, x + 2y = 168. Then, x + y + (168 - 126) = x + 2y. So, x + y + 42 = x + 2y. Then, 42 = x + 2y - x - y, So, 42 = y. Then x = 126 - 42, x = 84. To prove this. $5 x 84 = 420 and $10 x 42 = 420. 420 + 420 = 840.

[@panlomito]

5A +10B = 840 with A+B = 126 solves in (126-B).5 +10B = 840 resulting in B=42 and A=84... I prefer to keep it simple.

[@williambiggs3699]

I divided the total money (840$) by the all bills x 10$ (1260$) and found that 2/3 of the bills were 5$ bills. Therefore 1/3 of 126 = 42. And 42 x 10$ = 420$... And 84 x 5$ = 420$... And 420$ + 420$ = 840$. So there were 84 fives.

[@kevinwesterlund1495]

At about 6:40 you state (and write on the board) that the number of 5s plus the number of 10s is equal to 840. What kind of gibberish is that? It should be 5 times the number of fives plus 10 times the number of tens. Your incorrect statement throws confusion into a trivially easy problem.

[@t.daniel5003]

If you multiply $10.00 x80 = 800. That leaves 40. 40 ÷ 5.00 = 8?

[@stuc904]

S0 1x=£10 and 2x=£5 since its half of £10. so 1x + 2x =126 notes. so 3x = 126 which means x=42 . So 42x10 + 84 x 5 =£840

[@steveb6535]

This seems like a painfully complicated method of working out something you could feasibly do in your head. 126 bills: let's say they're all $5. This would give us $630. We need $210 more to get $840. This means we need to upgrade 210/5 of our bills from $5 to $10. This gives us 42 bills that need to be upgraded to $10, leaving 84 bills at $5.

[@russelllomando8460]

got it. great brain workout. thanks -- used algebra not Trial & Error.

[@toms6888]

Easy to do since 5 is half of 10. I know that 84 tens = $840. I subtracted 84 (tens)from the total bills (126) which is 42, and divided by half (which means multiply by 2)..... 84 fives . I doubt my reasoning is solid. But thats how I did it

[@stephencaldicott1529]

I did the algebra and got 84 5's, although, have I missed something in the question? 2 5's and 830 10's also solves the problem.

[@stephencaldicott1529]

Sorry, forget that, forgot the 126 notes element! 🙄

[@HeatherDiMarco]

There are 126 bills in total. Too many bills in your 2nd solution

[@MissJean63]

I used trial and error because Math is Figureoutable. (Kudos to Pam Harris).

[@brucemiller9285]

X+2x=126 where x is the number of 10s. 3x=126. X=42. There are 42 10s. Number of 5s is 126-42=84

[@MarcelDekker-il3vw]

840 - (126 x5) = 210 210/(10-5) = 42 so 42 10s.. = 420 and 126-42 = 84 fives. control 420 + 420 ... now mathematically maybe not correct. but for some odd reason I take always the lowest value and then see what is missing. hope to learn here another way

[@ab_ab_c]

It is correct & a good method to do in your head.

[@colleencurrier1586]

Eight tens and eight fives.

[@robertstuart6645]

Using systems of equations and Gaussian elimination works just as easy.

[@darkparker7500]

84 Five-dollar bills.

[@ab_ab_c]

The easiest way to solve & answer the problem is: Take 840/5=168 bills. Since 168>126 bills, we know that we need to convert some number of those fives into tens, hence: 168-126=42 bills. 42*10 = 420. 840-420=420. 420/5=84. Hence, we see that we need 42 tens & 84 fives. 42 bills + 84 bills = 126 bills Ed has 84 fives. ---------------------------- Alternatively, we could solve the problem using the following algebraic method: From the problem we can construct the following 2 equations: 1. some # of 5s + some # of 10s = 126 bills so: f + t = 126 or t = 126 - f (when solved for the unknown number of tens, which we will need below) 2. 5f + 10t = 840 (this means $5 * some # of fives + $10 * some number of tens = $840. Since we solved for t above (i.e. the unknown number to tens), we know that we can substitute 126 - f into equation 2 as follows: 5f + 10(126 - f) = 840 Then, :using algebra, we solve for f to determine the number of fives as follows: 5f + 1260 - 10f = 840 -5f = 840 - 1260 -5f = -420 f = -420/-5 f = 84 (this means that there are 84 fives) Then we use equation 1 to determine the number of tens as follows: t = 126 - f t = 126 - 84 t = 42 (this means that there are 42 tens) Then we check our answers to ensure they are correct using equation 2 as follows: 5(84) + 10(42) = 840 420 + 420 = 840 840 = 840 (this is true, so we know our answers are correct) Then we answer the problem question: "How many $5s does Ed have?" Ed has 84 fives.

[@bolek_lolek]

(5×(126-y))+10y=840 y=42 x=84

[@mariaolaciregui2128]

The $840. Will be 65 bills $10.00, and 38 bills of $5.00 . Totally $840.00 dollards.

[@HeatherDiMarco]

But only 103 bills used. Ed has 126 bills

[@deograciousuwiragiye8429]

Fives notes are 42 more than tens notes

[@li358690]

84 of $5 42 of $10

[@SPRoehl]

42 10s & 84 5s=840

[@kolkattaindia]

10x80=800, 5x8=40…800+40=840….

[@djohannsson8268]

Let x number of five dollar bills Let y number of ten dollar bills x + y = 126 5x + 10y = 840 Solve by term elimination. -5x + -5y = -630. *(-5) 5x + 10y = 840 ------- sum terms -------- 0x + 5y = 210 y = 210/5 = 42 Substitute y value into original equation x + 42 = 126. x= 126-42 = 84 Solve other half for fun x + y = 126. 5x + 10y = 840 -10x + -10y = -1260 I'm *(-10) 5x + 10y = 840 --------- sum ---------------- -5x + 0y = -420 x = -420 / -5 = 84

[@bullinmd]

Linear algebra.

[@DonovanSmith-ss7ro]

The answers are 42 and 84

[@apmcd47]

Is this easier? 5x + 10y = 840 -> x + 2y = 168. x + y = 126 -> 2x + 2y = 252. 2x + 2y - (x + 2y) = 252 - 168 -> 2x - x + 2y - 2y = 84 -> x = 84. The ys cancel out, leaving the x. No negative y and no conversion of y back to x. Of course, I had to redo this problem several times before I realised this solution.

[@StephenRayWesley]

53 31 (x+1x-53) (x+1x-31)

[@darellpiper7227]

84 Fives

[@gilbertrainey-bc2sg]

9 fives and 8 tens

[@stevewoodruff4175]

You made this unduly complicated. 840/126=6.6666667 126×.6666667=84 5's 5 second solve. You took 10 minutes. What's the point?

[@charlesmitchell5841]

So you have 84 fives and 42 tens. 😅

[@Bluuplanet]

84

[@JohnSmith-t1o4v]

28

[@sujathasankar8931]

Number of fives is 84.

[@mariaolaciregui2128]

Ed will have 38 bills of $5.00.

[@julianlayton9081]

None

[@jaybananas8157]

You’re very knowledgeable but your videos aren’t succinct at all. I enjoy your problems and would watch more of your videos if they were to the point.

[@preparados1917]

I skip the videos to the parts where the actual problem is worked. I do not watch the rest.

[@zztop6546]

Hey mate you babble on and on quite boring.

[@darkfreeway]

84

[@frankalfonso7070]

84

[@kristineg9816]

84