SOLUTION: Please help me solve this problem: A 210 ft. long rope is cut into 3 pieces. The first piece is 3 times as long as the second piece. The third piece is 2 times as long as the

Question 460756: Please help me solve this problem:
A 210 ft. long rope is cut into 3 pieces. The first piece is 3 times as long as the second piece. The third piece is 2 times as long as the second piece. What is the length of the longest piece of rope?
a. 70 ft
b. 90 ft
c. 105 ft
d. 110 ft
e. 140 ft
Thanks!!!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x, y, and z be the lengths of the three pieces of rope.

Since "The first piece is 3 times as long as the second piece", we know that .

"The third piece is 2 times as long as the second piece" tells us that .

Now since the three pieces were cut from a 210 ft rope, this means that

Now plug in and to get

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

This means that the second piece is 35 ft long.

Now plug this into to get . So the first piece (the longest piece) is 105 ft long.

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Answer:

The length of the longest piece of rope is 105 ft. So the answer is choice C)
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