Question

A 8 feet piece of PVC pipe is cut into three pieces the longest piece is 12 inches longer than the three times the smallest piece the middle piece is 5 inches less than the longest piece how long is each piece round your answer to the nearest inch if necessary

Answer 1

Variables

• x: length of the longest piece, in inches

,

• y: length of the middle piece, in inches

,

• z: length of the smallest piece, in inches

The addition of the three pieces makes the original piece of PVC pipe which is 96 in (equivalent to 8 ft) long, then:

x + y + z = 96 (eq. 1)

The longest piece is 12 inches longer than the three times the smallest piece, then:

x = 12 + 3z (eq. 2)

The middle piece is 5 inches less than the longest piece, then:

y = x - 5 (eq. 3)

Substituting equation 2 into equation 3 and combining similar terms:

y = 12 + 3z - 5

y = (12 - 5) + 3z

y = 7 + 3z (eq. 4)

Substituting equation 2 and equation 4 into equation 1, and combining similar terms:

12 + 3z + 7 + 3z + z = 96

(12 + 7) + (3z + 3z + z) = 96

19 + 7z = 96

Subtracting 19 at both sides of the equation:

19 + 7z - 19 = 96 - 19

7z = 77

Dividing by 7 at both sides of the equation:

`\begin{gathered} (7z)/(7)=(77)/(7) \\ z=11 \end{gathered}`

Substituting this result into equation 2:

x = 12 + 3z

x = 12 + 3*11

x = 12 + 33

x = 45

Substituting z = 11 into equation 4:

y = 7 + 3z

y = 7 + 3*11

y = 7 + 33

y = 40

Final answer

• length of the longest piece: 45 in

,

• length of the middle piece: 40 in

length of the smallest piece: 11 in