Colton has a change jar that contains $7.75 in half dollars and quarters. he has 13 more quarters than half dollars. how many of each type of coin does he have?

X= number of half dollars
x + 13= number of quarters

$0.50x + $0.25(x + 13)= $7.75

$0.50x + $0.25(x + 13)= $7.75
multiply 0.25 by parentheses

0.50x + (0.25 * x) + (0.25 * 13)= 7.75

0.50x + 0.25x + 3.25= 7.75
combine like terms

0.75x + 3.25= 7.75
subtract 3.25 from both sides

0.75x= 4.50
divide both sides by 0.75

x= 6 half dollars

QUARTERS
= x + 13
= 6 + 13
= 19 quarters

CHECK
$0.50x + $0.25(6 + 13)= $7.75
0.50(6) + 0.25(19)= 7.75
3 + 4.75= 7.75
7.75= 7.75

ANSWER: There are 6 half dollars and 19 quarters.

Hope this helps! :)

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.