Question

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

Answer 1

This is a problem that will use two equations.

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

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

Explanation:

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 `" "rarrD=103-Q`

Substitute `D` into the first equation.

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

`10.3-0.1Q+0.25Q=15.25`

`0.15Q=4.95`

`Q=33`

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

`D=70`

FINAL ANSWER:

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