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

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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) About Me  (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 x=3y.


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


Now since the three pieces were cut from a 210 ft rope, this means that x%2By%2Bz=210



Now plug in x=3y and z=2y to get 3y%2By%2B2y=210


6y=210 Combine like terms on the left side.


y=%28210%29%2F%286%29 Divide both sides by 6 to isolate y.


y=35 Reduce.


This means that the second piece is 35 ft long.


Now plug this into x=3y to get x=3%2835%29=105. 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)