Answer
The answer is: two 4 ft pieces and one 12 ft piece.
Work Step by Step
We assign the variables:
x = length of the longest piece
y = length of the each of the two equal pieces
Step 1:
Find the equations that represent the problem.
We know $x + 2y = 20$ because the addition of all three pieces has to equal the whole piece they were cut from.
$x+2y=20$ -> Eq. 1
We can get the second equation from the wording in the problem.
From "the longest piece will be three times as long as each of the other two of equal lengths", we get
$x=3y$ -> Eq. 2
Step 2:
Solve the system of equations. Using the substitution method:
-> Substitute Eq. 2 into Eq. 1
$3y+2y=20$
$5y=20$
$y=\frac{20}{5}$
$y=4$
-> Substitute the value for $y$ into Eq. 2
$x=3(4)$
$x=12$
Step 3:
The answer is: two 4 ft pieces and one 12 ft piece.
