SOLUTION: Tevin has a change jar that contains only pennies and dimes. He has 60 coins which add up to a total of $3.57. How many of each type of coin does he have?

Question 1185563: Tevin has a change jar that contains only pennies and dimes. He has 60 coins which add up to a total of $3.57. How many of each type of coin does he have?

Found 4 solutions by Alan3354, greenestamps, Theo, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Tevin has a change jar that contains only pennies and dimes. He has 60 coins which add up to a total of $3.57. How many of each type of coin does he have?
-------------------
p + d = 60
1p + 10d = 357
------------------- Subtract
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

The fastest way to find the answer is by logical reasoning with some simple mental arithmetic.

With a total value of #3.57, the number of pennies must be one of these numbers:

2, 7, 12, 17, ...

So try one of those and see if it works; then adjust if needed.

17 pennies would mean 60-17=43 dimes; $0.17+$4.30 = $4.47. Too much.

Maybe next try 37 pennies and 23 dimes: $2.30+$0.37 = $2.67. Too little.

Looking at those results and doing some easy calculations shows the correct total is exactly halfway between our two guesses.

So try 27 pennies and 33 dimes. $3.30+$0.27 = $3.57. Just right.

ANSWER: 33 dimes and 27 pennies

And here is another path that can teach you a good problem solving strategy when you are using guess-and-check.

After finding that 17 pennies and 43 dimes was $4.47, which is $0.90 too much, you can logically reason that exchanging a dime for a penny reduces the total value by $0.09. So to reduce the total $4.47 by $0.90 to get the correct total of $3.57, you need to exchange 10 dimes for pennies.

So the correct combination is 43-10=33 dimes and 17+10=27 pennies.

But probably a formal algebraic solution is wanted....

x = # of dimes
60-x = # of pennies

The total value is $3.57 = 357 cents

10x+1(60-x)=357
10x+60-x=357
9x=297
x=33

ANSWER: x=33 dimes, 60-x=27 pennies

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the change jar has 60 coins composed of pennies and dimes only.

you can work this problem in cents, or you can work this problem in dollars.

it makes a difference.

if you work this problem in dollars, then your equations are:

x + y = 60
.10x + .01y = 3.57

multiply both sides of the first equation by .10 and leave the second equation as is to get:

.10x + .10y = 6
.10x + .01y = 3.57

subtract the second equation from the first to get:

.09y = 2.43

solve for y to get:

y = 2.43 / .09 = 27

since x + y = 60, then x = 33.

confirm by replacing x and y in the original equations with 33 and 27 to get:

x + y = 33 + 27 = 60
.10x + .01y = .10*33 + .01*27 = 3.3 + .27 = 3.57

both of these equations confirm the value of x and y are good.

-----------------------------------------------------------------------

if you work this problem in cents, then your equations are:

x + y = 60
10x + y = 357

multiply both sides of the first equation by 10 and leave the second equation as is to get:

10x + 10y = 600
10x + y = 357

subtract the second equation from the first to get:

9y = 243

solve for y to get:

y = 243/9 = 27

since x + y = 60 then x = 33.

confirm the value are good by replacing x and y with 33 and 27.

x + y = 33 + 27 = 60
10x + y = 10*33 + 27 = 330 + 27 = 357

values of x and y are confirmed to be good.

the key is to determine whether you want to solve the problem in cents or in dollars.

if cents, then 3.57 becomes 357 cents and dimes becomes 10x and pennies become y

if dollars, then 3.57 is left as is and dimes becomes .10x and pennies become .01y

remember, x is the number of dimes and y is the number of pennies.

.10x gives you the value of the dimes in dollars.
.01y gives you the value of the pennies in dollars.

10x gives you the value of the dimes in cents.
y gives you thje value of the pennies in cents.
keep in mind that y means 1 * y which can also be shown as 1y.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Tevin has a change jar that contains only pennies and dimes. He has 60 coins which add up to a total of $3.57. How many of each type of coin does he have?

Let number of dimes be D Then number of pennies = 60 - D We then get: .1D + .01(60 - D) = 3.57 .1D + .6 - .01D = 3.57 .1D - .01D = 3.57 - .6 .09D = 2.97 Number of dimes, or You should now be able yo find the number of pennies. One of the other 3 people who responded makes this problem so COMPLEX and time-consuming when it shouldn't be. No-one wants to spend all that time trying to figure out just one problem especially if he/she is in an exam, which is usually timed.

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