Astudent makes a $10.50 purchase at the bookstore with a $20 bill. the store has no bills and gives the change in quarters and fifty-cent pieces. there are 30 coins in all. how many of each kind are there?

he collected 22 quarters and 8 fifty-cent pieces

Step-by-step explanation:

Given;

The total amount of money he is to collect is;

A = 20 - 10.50 = $9.50

Let x represent the number of quarter he collected.

Then the number of fifty-cent pieces he collected will be; 30-x

Therefore we can represent it with the equation below;

0.25x + 0.50(30-x) = 9.50

0.25x + 15 - 0.50x = 9.50

0.25x = 15-9.50

x = (15-9.50)/0.25

x = 5.50/0.25

x = 22

The number of fifty-cent is equal to;

30-x = 30-22 = 8

Therefore, he collected 22 quarters and 8 fifty-cent pieces