SOLUTION: PLEASE HELP ME SOLVE THIS PROBLEM A 210 FT LONG ROPE IS CUT IN 3 PIECES, THE FIRST PIECE OF ROPE IS 3 TIMES AS LONG AS THE SECOND PIECE OF ROPE. THE THIRD PIECE OF ROPE IS 2 TIME

Question 595920: PLEASE HELP ME SOLVE THIS PROBLEM
A 210 FT LONG ROPE IS CUT IN 3 PIECES, THE FIRST PIECE OF ROPE IS 3 TIMES AS LONG AS THE SECOND PIECE OF ROPE. THE THIRD PIECE OF ROPE IS 2 TIMES AS LONG AS THE SECOND PIECE OF ROPE WHAYT IS THE LEGTH OF THE LONGEST PIECE OF ROPE

Found 2 solutions by dfrazzetto, mamiya:
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!
Total length = 210
first piece = 3(second piece) = 3x
second piece = x
third piece = 2(second piece) = 2x
All pieces must add to total length:
3x + x + 2x = 210
6x = 210
x = 35
Longest piece is first piece = 3x = 3(35) = 105
Answer by mamiya(56) (Show Source): You can put this solution on YOUR website!

Let X be the length of the first of rope ; Y the length of the second and Z the length of the third.
By understanding the first data, we know that x+y+z = 210
The first piece of rope is 3 times as long as the second piece of rope, means x= 3y
The third piece of rope is 2 times as long as the second piece of rope , means z= 2y
x+y+z = 210
so we get this system of equations x= 3y
z= 2y
by plugging the two last equation in the first one, we get
x+y+z = 210 --> 3y+y+2y=210
--> 6y= 210
--> (6y)/6 = 210/6
--> y = 35
we know x = 3y = 3 * 35 = 105
we know z = 2y = 2*35 = 70
so the length of the longest piece of rope is 105 ft

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