Question

A pipe is to be cut up such that the second piece is 3 inches shorter than the first and the third piece is
four inches more than the first. How long is each piece if the pipe is 84 inches long?

Answer 1

Answer:

$F = 27\frac{2}{3}$

$S = 24\frac{2}{3}$

$T = 31\frac{2}{3}$

Step-by-step explanation:

Represent the first piece with F, the second with S and the third with T.

So:

$S = F - 3$

$T =4+ F$

$S + T + F = 84$

Required

Find the length of each piece

Substitute $S = F - 3$ and $T =4+ F$ in $S + T + F = 84$

$F - 3 + 4 + F + F = 84$

Collect like terms

$3F = 84 + 3 - 4$

$3F = 83$

Divide through by 3

$F = \frac{83}{3}$

$F = 27\frac{2}{3}$

Substitute $F = 27\frac{2}{3}$ in $S = F - 3$ and $T =4+ F$

$S = F - 3$

$S = 27\frac{2}{3} - 3$

$S = 24\frac{2}{3}$

$T =4+ F$

$T = 4 + 27\frac{2}{3}$

$T = 31\frac{2}{3}$