Jeremy has 24 quarters and half dollars. If he had twice as many half dollars and half as many quarters, he would have $2 more. How much money does he have?

ACTUAL

"IF"

Number

Value

Total Value

Number

Value

Total Value

Quarters

n

25

25n

n/2

25

25n/2

Half $$

24 - n

50

1200 - 50n

48 - 2n

50

2400 - 100n

Note: For the "IF" column, there are half the number of quarters and twice as many half dollars.

Fact for Equation: "IF" amount is $2.00 (200 cents!) more than the "Actual" amount.

25n/2 + 2400 - 100n = 25n + 1200 - 50n + 200

12.5n + 2400 - 100n = -25n + 1400

-87.5n + 2400 = -25n + 1400

-62.5n + 2400 = 1400

-62.5n = -1000

n = 16

Answer: He has 16 quarters and 8 half dollars.

He has $4.00 + $4.00

He has a total of $8.00