Question

Melo has 600 quarters and dimes in his piggy bank. When he broke open his piggy bank, he found out he hdd a total of $123.75. How many quarters did he have?

Answer 1

X= # quarters
y= # dimes

QUANTITY EQUATION
x + y= 600

COST EQUATION
$0.25x + $0.10y= $123.75

STEP 1
Solve for one variable in the quantity equation

x + y= 600
subtract y from both sides
x= 600 - y

STEP 2
substitute x= 600-y in cost equation

$0.25x + $0.10y= $123.75
0.25(600-y) + 0.10y= 123.75
(0.25*600) + (0.25*-y) + 0.10y= 123.75
150 - 0.25y + 0.10y= 123.75
150 - 0.15y= 123.75
subtract 150 from both sides
-0.15y= -26.25
divide both sides by -0.15
y= 175 dimes

STEP 3
Substitute y= 175 in either equation to solve for number of quarters

x + y= 600
x + 175= 600
subtract 175 from both sides
x= 425 quarters

CHECK:
$0.25x + $0.10y= $123.75
0.25(425) + 0.10(175)= 123.75
106.25 + 17.50= 123.75
123.75= 123.75

ANSWER: There are 425 quarters

Hope this helps! :)

Answer 2

Well 123.75 divided by 0.25 is 495 so he had 495 quarters