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Sagot :
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:
[tex]\begin{gathered} \frac{7z}{7}=\frac{77}{7} \\ z=11 \end{gathered}[/tex]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
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