HELP!!!!! MATH QUESTION

Question

A woman has 21 total coins in her pocket, all of which are either dimes or quarters. If the total value of her change is $3.90, how many dimes and how many quarters does she have?

Write the number of dimes, then the number of quarters separated by a comma.

Answer 1

Hi, Hayley.

Hopefully you already figured out the answer to this question, but just in case you didn't:

She has 21 coins in her pocket...dimes and quarters. Let us call the number of dimes (D) and the number of quarters (Q).

D + Q = 21

Therefore, we can write the number of dimes D = 21 - Q

Also, since each dime is worth $0.10 and each quarter is worth $0.25, we can also write:

.10D + .25Q = 3.90

Now we can substitute D = 21 - Q into the above equation:

.10(21 - Q) + .25Q = 3.90

2.10 - .10Q + .25Q = 3.90

.15Q = 3.90 - 2.10

.15Q = 1.80

Q = 12

Therefore, the number of quarters is 12

So, if D = 21 - 12, then D = 9

Since it says write the number of dimes, then the number of quarters separated by a comma, your answer is:

9, 12

Now, check your answer:

.10(9) + .25(12) = .90 + 3.00 = $3.90

The answer is correct