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- anonymous

A 30 ft piece of rope is cut into three sections such that the length of the second section is one ft more than the first section and the length of the third section is one ft less than three times the first. Find the lengths of the three sections......please help.

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- anonymous

- katieb

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- anonymous

say the length of the first section is L ft. long. what can you tell me about the lengths of section 2 and section 3?

- anonymous

The way you begin is to decide which section gets x. In the first sentence you see the length of the second section is..... and the length of the third section is.....
YOU NEVER SEE the length of the first section is.... so that is the section that gets the "x"

- anonymous

Thats all the problem says.....where do I begin?

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- anonymous

first section = x
second section = x + 1 (one foot more than the first section)
third section = 3x - 1 ( one foot less than three times the first section)

- anonymous

If you add the three sections together you get the entire rope which is 30 ft.

- anonymous

So
x + x + 1 + 3x - 1 = 30

- anonymous

Add like terms.
5x = 30 (x + x + 3x = 5x and 1 - 1 = 0)

- anonymous

I follow...

- anonymous

5x = 30
x = 6 Divide by 5 on both sides.

- anonymous

ok

- anonymous

first section = x which is 6ft
second section = x + 1 which is 6 + 1 = 7 ft.
third section = 3x - 1 which is 3(6) - 1 = 18 - 1 = 17 ft.
6 + 7 + 17 = 30 ft.

- anonymous

ok :) thanks so very much!

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