d= half dollars
q= quarters
Half dollars + quarters = 30 coins
d+q=30
Step 1:
Solve for one variable:
d+q=30
Subtract q from both sides
d=30-q
Step2:
Find quantity of each coin
d= $0.50
q= $0.25
0.50d+0.25q= $8.75
Substitute d=30-q for d in this equation
0.50(30-q)+0.25q= 8.75
15-0.50q+0.25q= 8.75
15-0.25q= 8.75
Subtract 15 from both sides
-0.25q= -6.25
Divide both sides by -0.25
q= 25 number of quarters
Substitute q=25 in equation to find d
d+q=30
d+25=30
Subtract 25 from both sides
d=5 number of half dollars
Check:
0.50d+0.25q= $8.75
0.50(5)+0.25(25)= 8.75
2.50+6.25= 8.75
$8.75=$8.75
Hope this helps! :)