Question

Byron has 72 coins in his piggy bank. The piggy bank contains only dimes

and quarters. If he has $14.70 in his piggy bank, which equation can be
used to determine q, the number of quarters he has?
(1) 14.70 + 0.25q = 72
(2) 0.10(q - 72) + 0.25q = 14.70
(3) 0.10(72 - q) + 0.25q = 14.70
(4) 0.10q + 0.25(72 - q) = 14.70

Answer 1

(3)
`0.25q+0.10(72-q)=14.70`

Explanation:

Let d represent number of dimes and q represent number of quarters.

We have been given that Byron has 72 coins in his piggy bank. We can represent this information in an equation as:

`q+d=72...(1)`

We are also told that the value of all coins is $14.70.

Value of d dimes:
`0.10d`.

Value of q quarters:
`0.25q`.

`0.25q+0.10d=14.70...(2)`

From equation (1), we will get:

`d=72-q`

Substitute this value in equation (2):

`0.25q+0.10(72-q)=14.70`

Therefore, the equation
`0.25q+0.10(72-q)=14.70` can be used to determine q, the number of quarters.