Question

A bag containing thirty coins all of which are either quarters or dimes. If the
total value of the coins is $5.85, how many of each
kind are there?

Answer 1

Answer/Step-by-step explanation:

Q=number of quarters; D=number of dimes

Q+D=30

D=30-Q . Use this to substitute for D below

$0.10D+$0.25Q=$5.85 . Substitute for D from above.

$0.10(30-Q)+$0.25Q=$5.85

$3.00-$0.10Q+$0.25Q=$5.85

$0.15Q=$2.85

Q=19

ANSWER 1: There were 19 quarters.

D=30-Q=30-19=11

ANSWER 2: There were 11 dimes.

CHECK:

$0.10D+$0.25Q=$5.85

$0.10(11)+$0.25(19)=$5.85

$1.10+$4.75=$5.85