Answer :
Answer:
$76
Step-by-step explanation:
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.
