Question

At first, the ratio of Dave's savings to Sam's savings was 5:4. After each of them donated $40 to charity, the ratio of Dave's savings to Sam's savings became 13:10. What was Dave's savings at first?

Answer 1

$300

Explanation:

Let D = Dave's savings and S = Sam's savings.

(1) D/S = 5/4

(2) (D – 40)/(S-40) = 13/10 Multiply (1) by 4S

(3) 4D = 5S Multiply (2) by 10(S-40)

10(D - 40) = 13(S - 40) Remove parentheses

(4) 10D – 400 = 13S - 520 Solve (3) for S

S = (4/5)D Substitute into (4)

10D – 400 = 13(4/5)D - 520 Multiply each side by 5

50D – 2000 = 52D – 2600 Subtract 50D from each side

-2000 = 2D – 2600 Add 2600 to each side

600 = 2D Divide each side by 2

D = $300

Dave's savings at first were $300.