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

`F = 27(2)/(3)`

`S = 24(2)/(3)`

`T = 31(2)/(3)`

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 = (83)/(3)`

`F = 27(2)/(3)`

Substitute
`F = 27(2)/(3)` in
`S = F - 3` and
`T =4+ F`

`S = F - 3`

`S = 27(2)/(3) - 3`

`S = 24(2)/(3)`

`T =4+ F`

`T = 4 + 27(2)/(3)`

`T = 31(2)/(3)`