Answer
The answer is: one piece that is 81 inches and the other that is 63 inches.
Work Step by Step
We assign the variables:
x = piece #1
y = piece #2
Step 1:
Find the equations that represent the problem.
We know $x+ y = 12$ because the addition of the two pieces cut has to equal the total length of the beam.
In our case, we will use the measurement in inches to have everything in the same units. Remember $1~ft = 12~inches$.
$x+y=12$ in feet
$x+y=144$ -> Eq. 1 (in inches)
We can get the second equation from the wording in the problem.
From "one piece is 18 in. longer than the other ", we get
$x=y+18$ -> Eq. 2
Step 2:
Solve the system of equations using the substitution method,
-> Substitute Eq. 2 into Eq. 1
$y+18+y=144$
$2y=144-48$
$2y=126$
$y=\frac{126}{2}$
$y=63$ inches
-> Substitute the value for $y$ into Eq. 2
$x=63+18$
$x=81$ inches
Step 3:
The answer is: one piece that is 81 inches and the other that is 63 inches.
