Laura and drew went shopping together. Ratio of money laura brought to the money drew brought was 5:7. After they each spent $76, the ratio od money they had left was 3:5. How much more money does Drew have than Laurah

Given the initial ratio of Laura's money to Drew's money is 5:7, and it is reduced to 3:5 after each spends $76, you want to know how much more Drew has than Laura.

Setup

Let L and D represent the money Laura and Drew have to start. The given relations tell us ...

[tex]\dfrac{L}{D}=\dfrac{5}{7}\\\\\\\dfrac{L-76}{D-76}=\dfrac{3}{5}[/tex]

Solution

Cross-multiplying each equation gives ...

7L = 5D
5(L -76) = 3(D -76)

Rearranging, we have ...

5D -7L = 0

3D -5L = -2(76)

Subtracting the second of these equations from the first gives ...

(5D -7L) -(3D -5L) = (0) -(-2)(76)

2D -2L = 2(76) . . . . . . . simplify

D -L = 76 . . . . . . . . . . . . divide by 2

Drew has $76 more than Laura.

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Additional comment

Often, it works well to consider the ratio units. Here, the spending reduces each of the ratio units by 2: 5→3, 7→5. The initial and final difference between the ratio units are both 2: 7-5=2, 5-3=2. This suggests the difference is equal to the spending, $76.