SOLUTION: A 174-meter rope is cut into two segments. The longer segment is 30 meters longer than the shorter segment. Write and solve a linear equation to find the length of each segment.

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Question 1186778: A 174-meter rope is cut into two segments. The longer segment is 30 meters longer than the shorter segment.
Write and solve a linear equation to find the length of each segment. Include units.
The segments are ___ and ___ long.
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.

Let x be the length of the shorter segment, in meters.

Then the length of the longer segment is (x+30) meters.


The total length is 174 meters, giving an equation


    x + (x+30) = 174.


Simplify and find x


    2x + 30 = 174

    2x = 174 - 30

    2x = 144

     x = 144/2 = 72.


ANSWER.  One piece is 72 meters; another piece is 72 + 30 = 102 meters.


CHECK.  72 + 102 = 174.   ! Correct !

Solved.



Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

A -meter rope is cut into two segments.
The longer segment is meters longer than the shorter segment.

Write and solve a linear equation to find the length of each segment. Include units.
let the shorter segment be , then longer segment is
together, both measure
solve for



so, the shorter segment is , then longer segment is
The segments are ___ and ___ long.


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