A window cleaner has enough supplies to clean 21 windows per office building on a certain number of buildings. They can also clean the windows of a school with 42 windows. Altogether, there are enough supplies to clean 126 windows. How many office buildings can be cleaned?

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

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

To solve this problem, let's identify what we need to find and the information given:

1. What we need to find: The number of office buildings that can be washed.

2. Information given:
- Each office building has 21 windows.
- A school has 42 windows.
- There are enough supplies to clean 126 windows in total.

3. Setting up an equation:
- Let [tex]$ x $[/tex] represent the number of office buildings.
- The total number of windows from the office buildings will be [tex]$ 21x $[/tex] since each office building has 21 windows.
- Adding the 42 windows of the school, the total number of windows to clean is [tex]$ 21x + 42 $[/tex].

4. Equation to solve:
[tex]\[
21x + 42 = 126
\][/tex]

5. Solve the equation step-by-step:

- Subtract 42 from both sides to isolate the term with [tex]$ x $[/tex]:
[tex]\[
21x = 126 - 42
\][/tex]
[tex]\[
21x = 84
\][/tex]

- Divide both sides by 21 to solve for [tex]$ x $[/tex]:
[tex]\[
x = \frac{84}{21}
\][/tex]
[tex]\[
x = 4
\][/tex]

6. Conclusion: The number of office buildings that can be washed is 4.