Question

Sally has a total of 40 quarters and dimes worth $6.55. How many of each does she have?

Answer 1

Sally has 23 dimes worth $2.30 and 17 quarters worth $4.25

Explanation:

Let's call the number of dimes Sally has `d` and the number of quarters Sally has `q`.

We can then write these two equations from the information given in the problem:

`d + q = 40`

`0.1d + .025q = 6.55`

Step 1) Solve the first equation for `d`:

`d + q - q = 40 - q`

`d + 0 = 40 - q`

`d = 40 - q`

Step 2) Substitute `40 - q` for `d` in the second equation and solve for `q`:

`0.1(40 - q) + 0.25q = 6.55`

`4 - 0.1q + 0.25q = 6.55`

`4 + 0.15q = 6.55`

`4 - 4 + 0.15q = 6.55 - 4`

`0 + 0.15q = 2.55`

`0.15q = 2.55`

`(0.15q)/0.15 = 2.55/0.15`

`q = 17`

Step 3) Substitute `17` for `q` into the solution to the first equation in Step 1) and calculate `d`;

`d = 40 - 17`

`d = 23`