Question

A 7 foot piece of PVC pipe is cut into three pieces. The longest piece is 13 inches longer than three times the smallest piece. The middle piece is 5 inches less than the longest piece. How long is the middle piece? Round your answers to the nearest inch, if necessary.

Answer 1

Let x represent length of smallest piece.

We have been given that the longest piece is 13 inches longer than three times the smallest piece. So length of longest piece would be $3x+13$.

The middle piece is 5 inches less than the longest piece. So length of middle piece would be $3x+13-5=3x+8$.

We have been given that the length of pipe is 7 foot.

1 feet = 12 inches.

7 feet = 7*12 inches = 84 inches.

Now we will equate the sum of lengths of 3 pipes with 84 as:

$x+3x+13+3x+8=84$

Let us solve for x.

$7x+21=84$

$7x+21-21=84-21$

$7x=63$

$\frac{7x}{7}=\frac{63}{7}$

$x=9$

Length of middle piece would be $3x+8\Rightarrow 3(9)+8=27+8=35$.

Therefore, the middle piece is 35 inches long.