SOLUTION: please help my problem solving. (a 165 rope is cut into 3 pieces, the second piece is twice as long as the first. the third is 4 times as long as the second. how long is each piece

Question 114708: please help my problem solving. (a 165 rope is cut into 3 pieces, the second piece is twice as long as the first. the third is 4 times as long as the second. how long is each piece of rope?) thank you
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let x represent the length of the first piece of rope.
.
The second piece of rope is twice as long as the first piece. Therefore, the length of
the second piece is 2*x.
.
The third piece is 4 times as long as the second piece. So it is 4 times 2*x which is 8*x
in length.
.
The lengths of all three pieces add up to be 165. In equation form this means that:
.
x + 2x + 8x = 165
.
Adding all three terms on the left side results in:
.
11x = 165
.
Solve for x by dividing both sides of this equation by 11 and the equation becomes:
.
x = 165/11 = 15
.
This means the length of the first piece is 15. The second piece is twice that, so the
length of the second piece is 30. And the third piece is 4 times as long as the second piece
so the length of the third piece is 4 times 30 or 120.
.
In summary, the three pieces are 15, 30, and 120 in length.
.
Check: do 15, 30, and 120 add up to 165? Yes, they do ... and they meet the requirements
that the second is twice the first and the third is four times the second. The answer checks.
.
Hope this helps you to understand the problem and how to solve it.
.
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