SOLUTION: A scout leader wishes to cut a rope for tents into three pieces whose lengths are consecutive odd integers. If the length of the first and the third piece is 58 feet, find the leng

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A scout leader wishes to cut a rope for tents into three pieces whose lengths are consecutive odd integers. If the length of the first and the third piece is 58 feet, find the leng      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 335846: A scout leader wishes to cut a rope for tents into three pieces whose lengths are consecutive odd integers. If the length of the first and the third piece is 58 feet, find the length of the middle piece. Thanks for your help!!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the lengths are consecutive odd integers.

if the first length is n, then the second length is n+2, and the third length is n + 4.

The sum of the lengths of the first and the third piece is 58 feet.

This means that n + n + 4 = 58.

Combine like terms to get:

2n + 4 = 58.

Subtract 4 from both sides of the equation to get:

2n = 54.

Divide both sides of the equation by 2 to get:

n = 27.

Since these are 3 consecutive numbers that are all odd, this means that:

first number is n = 27
second number is n + 2 = 29
third number is n + 4 = 31

sum of first and third number is 27 + 31 = 58.

Everything checks out so this is your answer.