Answer
164 fluorescent light fixtures and 92 incandescent light fixtures
Work Step by Step
Assign the variables:
x = number of fluorescent light fixtures
y = number of incandescent light fixtures
$\textbf{Step 1:}$
Find the equations that represent the problem.
We know $x+y=256$, because the addition of the fluorescent fixtures and the incandescent fixtures has to equal the total light fixtures.
$x+y=256$ $\leftarrow$ Eq. 1
We can get the second equation from the wording in the problem.
"The number of fluorescent light fixtures will be 20 fewer than twice the number of incandescent light fixtures."
$x=2y-20$ $\leftarrow$ Eq. 2
$\textbf{Step 2:}$
Solve the system of equations. Using the substitution method,
$x+y=256$
$2y-20+y=256$
$3y=256+20$
$3y=276$
$y=\frac{276}{3}$
$y=92$
Now solve for x
$x+y=256$
$x+92=256$
$x=256-92$
$x=164$
$\textbf{Step 3:}$
The answer is 164 fluorescent light fixtures and 92 incandescent light fixtures.
