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! :)
