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.

Question

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.

anonymous · Answer

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 · Answer

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 · Answer

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

anonymous · Answer

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 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

I follow...

anonymous · Answer

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

anonymous · Answer

ok

anonymous · Answer

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 · Answer

ok :) thanks so very much!