A window cleaner has enough supplies to clean 21 windows per office building and the windows of a school with 42 windows. Altogether, there are enough supplies to clean 126 windows. How many office buildings can be washed?

Identify the equation that would be used to solve this problem algebraically.

A. [tex]21x - 42 = 126[/tex]
B. [tex]21x + 42 = 126[/tex]
C. [tex]42x - 21 = 126[/tex]
D. [tex]42x + 21 = 126[/tex]

To solve this problem, we need to find out how many office buildings can be washed with the available supplies when a school with 42 windows is also being cleaned. Altogether, there are enough supplies to clean a total of 126 windows.

Let's break it down step by step:

1. Define Variables:
- Let [tex]$ x $[/tex] represent the number of office buildings.
- Each office building has 21 windows.

2. Set Up the Equation:
- The cleaner can wash the windows of the office buildings and the school.
- The total number of windows that can be washed (from both the office buildings and the school) is 126.
- So, the equation accounting for both the office buildings and the school is:
[tex]\[
21x + 42 = 126
\][/tex]

3. Solve the Equation:
- First, subtract 42 (the number of windows in the school) from both sides to focus on the office buildings:
[tex]\[
21x = 126 - 42
\][/tex]
[tex]\[
21x = 84
\][/tex]
- Next, divide both sides by 21 to solve for [tex]$ x $[/tex]:
[tex]\[
x = \frac{84}{21}
\][/tex]
[tex]\[
x = 4
\][/tex]

Therefore, 4 office buildings can be washed with the available supplies. The correct equation to use for solving this problem is:
[tex]\[
21x + 42 = 126
\][/tex]