Question 460756
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+y+z=210}}}




Now plug in {{{x=3y}}} and {{{z=2y}}} to get {{{3y+y+2y=210}}}



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



{{{y=(210)/(6)}}} 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(35)=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)