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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?

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Answer:

$300  

Step-by-step 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.

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