A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar?

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Answer 1 · 2017-04-18T14:17:41

This is a problem that will use two equations.

$D = number of dimes and Q = number of quarters$ $D= " number of dimes and " Q = " number of quarters"$

There are $70 dimes and 33 quarters$ $70 " dimes " and 33 " quarters"$

0.1D+0.25Q=15.25

(This is because a dime is worth $0.10 and a quarter is worth $0.25.)

D+Q=103 $\to D = 103 - Q$ $" "rarrD=103-Q$

Substitute $D$ $D$ into the first equation.

$0.1 (103 - Q) + 0.25 Q = 15.25$ $0.1(103-Q)+0.25Q=15.25$

$10.3 - 0.1 Q + 0.25 Q = 15.25$ $10.3-0.1Q+0.25Q=15.25$

$0.15 Q = 4.95$ $0.15Q=4.95$

$Q = 33$ $Q=33$

Substitute for $Q$ $Q$ into the second equation.
$D + 33 = 103$ $D+33=103$

$D = 70$ $D=70$

FINAL ANSWER:

There are $70 dimes and 33 quarters$ $70 " dimes " and 33 " quarters"$