Question

Shehkar pulls 31 coins out of his pocket. each coin is either a dime or a quarter. if he has a total of 5.95, how many dimes does he have?

Answer 1

`12` dimes (and `19` quarters)

Explanation:

Define
`color(white)("XXX")d =` number of dimes
`color(white)("XXX")q =` number of quarters

We are told:
[1]`color(white)("XXX")d+q=31`
[2]`color(white)("XXX")10d+25q=595`

Multiply [1] by `10`
[3]`color(white)("XXX")10d+10q=310`

Subtract [3] from [2]
[4]`color(white)("XXX")15q=285`

Divide [4] by `15`
[5]`color(white)("XXX")q=19`

Substitute `19` from [5] for `q` in [1]
[6]`color(white)("XXX")d+19=31`

Subtract `19` from both sides of [6]
[7]`color(white)("XXX")d=12`