A jar contains half dollars and quarters. There are 30 coins in all in the jar. The total value of the coins is 8.75. How many half dollars are in the jar? To

Question

A jar contains half dollars and quarters. There are 30 coins in all in the jar. The total value of the coins is 8.75. How many half dollars are in the jar? 

Answer 1

Two equations are needed to solve this problem.

 

1. we know that there are 30 coins, so let h = number of half dollars, and q = number of quarters

so, h + q = 30

 

2. the dollar value of the coins is $8.75

let's convert the coin values into decimals, so 50 cents = $0.50, and 25 cents = $0.25

so $0.50h + $0.25q = $8.75

 

3. then, we can solve equation 1 for h = 30 - q, and substitute that value into equation 2

which becomes $0.50(30 - q) + $0.25q = $8.75

 

4. when you solve equation 3, you will have the number of quarters, which, when subtracted from 30, will give you the number of half dollars.