Question

Sue has 100 dimes and quarters. If the total value of the coins is $21.40, how many of each of kind of coin does she have?

Answer 1

Sue has `24` dimes and `76` quarters.

Explanation:

Let `d` be the number of dimes Sue has and let `q` be the number of quarters. As she has `2140` cents total, a dime is worth `10` cents, and a quarter is worth `25` cents, we obtain the following system of equations:

`{(d + q = 100), (10d + 25q = 2140):}`

From the first equation, we have `d = 100 - q`

Substituting that into the second equation, we have

`10(100-q) + 25q = 2140`

`=> 1000 - 10q + 25q = 2140`

`=> 15q = 1140`

`=> q = 1140/15 = 76`

Knowing that `q=76` we can substitute that value into the first equation to obtain

`d + 76 = 100`

`:. d = 24`

Thus, Sue has `24` dimes and `76` quarters.