A segment is divided into two parts having lengths in the ratio of 5:3. If the difference between the length of the parts is 6", find the length of the longest part.

15"

Explanation:

Let x be the length of the longer part, then the length of the shorter part is 3x/5, or also x - 6

therefore we have the following equation:

3x/5 = x - 6

We can multiply both sides by 5

3x = 5x - 6*5

2x = 30

x = 30/2 = 15"

So the length of the longer part is 15"

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