Question

Last month David and Mary saved some money in a ratio of 3:5. This month they saved an additional $154 together, and David now has three times as much money as he had last month and Mary has two times as much as she had last month. How much money did they save last month?

Answer 1

• David: $42
• Mary: $70

Explanation:

The two relations can be translated to a system of linear equations in two variables. These can be solved in any of the usual ways.

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setup

Let d and m represent the amounts David and Mary saved last month, respectively.

The first relation tells us

d/m = 3/5 ⇒ 5d = 3m ⇒ 5d -3m = 0

The second relation tells us that adding 3 times what David had last month to 2 times what Mary had last month will give a total that is 154 greater than the sum of their funds last month.

d +m + 154 = 3d +2m ⇒ 2d +m = 154

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solution

We can add 3 times the second equation to the first to eliminate m.

(5d -3m) +3(2d +m) = (0) +3(154)

11d = 462 . . . . . . . . simplify

d = 42 . . . . . . . . . divide by 11

Using the second equation, we can find Mary's savings:

m = 154 -2d

m = 154 -2(420 = 70

David saved $42 last month; Mary saved $70.