Question

When Jon went running in the park, he found 9 coins worth a total of $1.80. The coins were quarters and dimes. How many of each did he find?

Answer 1

Jon found 6 quarters and 3 dimes.

Explanation:

First, let's call the number of dimes Jon found `d` and the number of quarters Jon found `q`

We can now write the following equation:
`d + q = 9`

And, because dimes are worth $0.10 and quarters are worth $0.25 we can write:

`0.1d + 0.25q = 1.80`

Solving the first equation for `d` gives:

`d + q - q = 9 - q`

`d + 0 = 9 - q`

`d = 9 - q`

We can now substitute `9 - q` for `d` in the second equation and solve for `q`:

`0.1(9 - q) + 0.25q = 1.80`

`0.9 - 0.1q + 0.25q = 1.80`

`0.9 + 0.15q = 1.80`

`0.9 - 0.9 + 0.15q = 1.80 - 0.9`

`0 + 0.15q = 0.9`

`0.15q = 0.9`

`(0.15q)/0.15 = 0.9/0.15`

`q = 6`

We can now substitute `6` for `q` in solution to the first equation and calculate `d`:

`d = 9 - 6`

`d = 3`