x= dimes
y= quarters
QUANTITY EQUATION:
x+y=100
COST EQUATION:
$0.10x+$0.25y=$21.40
STEP 1:
Solve for one variable in quantity equation.
x+y=100
subtract y from both sides
x= 100-y
STEP 2:
Substitute answer above in cost equation.
Dimes= $0.10
Quarters= $0.25
(Value of dime * dime quantity) + (value of quarter * quarter quantity)= total value
$0.10x+$0.25y=$21.40
0.10(100-y) + 0.25y=21.40
multiply 0.10 by all in parentheses
(0.10*100)+(0.10*-y) + 0.25y= 21.40
10 - 0.10y + 0.25y= 21.40
10 + 0.15y= 11.40
subtract 10 from both sides
0.15y= 11.40
divide both sides by 0.15
y= 76 number of quarters
STEP 3:
substitute y=76 in either equation.
x+y=100
x+76=100
subtract 76 from both sides
x= 24 number of dimes
Hope this helps! :)
