Question

a piggy bank contains $5.45 in dimes and quarters. If the bank contains 29 coins, how many quarters are in the bank

Answer 1

Call the number of dimes
`d` and the number of quarters
`q`.

We know that:

`d+q=29`

and

`0.10d+0.25q=5.45`

By substitution:

`d=29-q`

`0.10(29-q)+0.25q=5.45`

`2.9-0.10q+0.25q=5.45`

`0.15q=2.55`

`q=(2.55)/(0.15)`

`q=17`

There are 17 quarters in the bank.

The question doesn't ask for it but we can also show that:

`d=29-q`

`d=29=17`

`d=12`

There are 12 dimes in the bank.