Coin Problem Example

There are 37 dimes and quarters in all. The combined value of the dimes and quarters is $4.60. How many dimes are there?

Find DIMES

Let D=DIMES

Let Q=QUARTERS

Let V=VALUE

Given D+Q=37

Given 4.6=0.1D+0.25Q

4.6=0.1(37-Q)+0.25Q Comment: Substitute 37-Q for D in 4.6=0.1D+0.25Q

4.6=3.7-0.1Q+0.25Q

0=-0.9-0.1Q+0.25Q

Solution Q=6 Comment

Solution D=31 Substitute Q=6 into D=37-Q

End