A 80 -foot piece of siding is cut into three pieces so that the second piece is four times four times as long as the first piece and the third piece is five times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.

Question

Mathematics

Maryjane Terry

19 June, 07:32

A 80 -foot piece of siding is cut into three pieces so that the second piece is four times four times as long as the first piece and the third piece is five times as long as the first piece. If x represents the length of the first piece, find the lengths of all three pieces.

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Answers (1)

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Sharon Moran · Answer 1

Lengths of the three parts are 8 foot, 32 foot and 40 foot respectively.

Step-by-step explanation:

We are given a 80 foot piece, which is cut into three parts,

Let, the length of the first part = x foot

As, the second piece is four times the length of the first piece.

The length of the second piece = 4x foot.

Also, the third piece is five times as long as the first piece.

So, the length of the third piece = 5x foot.

Thus, we get the equation,

x + 4x + 5x = 80

i. e. 10x = 80

i. e x = 8

Thus, the length of the first piece is 8 foot.

So, the length of second and third piece are 4*8 = 32 and 5*8 = 40 foot respectively.

Hence, the lengths of the three parts are 8 foot, 32 foot and 40 foot respectively.