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## Sagot :

**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**.

__

*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.