Question

A collection of quarters and nickels is worth $14.80. There are 88 coins in all.

How many of each coin are there?

Answer 1

Let x and y be the number of quarters and nickels.

We have x+ y= 88 (because there are 88 coins in total)
⇒ y= 88-x

On the other hand, we have: 25 cents*x+ 5 cents*y= 1,480 cents ($14.80= 1,480 cents)
⇒ 25x+ 5y= 1,480 (1)

Plug y= 88-x in (1), we have:
25x+ 5(88-x)= 1,480
⇒ ...
⇒ x= 52.

y= 88-52= 36

There are 52 quarters and 36 nickels~