Question

Ginny's piggybank contained $8.80 in quarters, dimes, and nickels. there were two more than five times as many nickels as quarters and 4 less than twice as many dimes as quarters. how many of each kind of coin was there in the bank?

Answer 1

There are 13 quarters, 67 nickels, and 22 dimes.

Explanation:

The value of a quarter is $0.25, the value of dime is $0.10, and the value of a nickel is $0.05. Let there be q quarters, n nickels, and d dimes.

Let's write equations from the statements given:

"Ginny's piggybank contained $8.80 in quarters, dimes, and nickels.":

`0.25q+0.1d+0.05n=8.80`

"there were two more than five times as many nickels as quarters":

`5q+2=n`

"4 less than twice as many dimes as quarters":

`2q-4=d`

Plugging in equation 2 and 3 into equation 1, we can solve for q:

`0.25q+0.1(2q-4)+0.05(5q+2)=8.80\\0.25q+0.2q-0.4+0.25q+0.1=8.80\\0.7q=8.80+0.4-0.1\\0.7q=9.1\\q=(9.1)/(0.7)=13`

Substituting q = 13 into equation 2 will give us nickels:

`n=5q+2\\n=5(13)+2\\n=67`

Substituting q = 13 into equation 3 will give us dimes:

`d=2q-4\\d=2(13)-4\\d=22`

There are 13 quarters, 67 nickels, and 22 dimes.