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 given the number of windows that can be cleaned with the available supplies.

Let's break it down:

1. Understand the Problem:
- We can clean 126 windows in total.
- Each office building has 21 windows.
- There is also a school with 42 windows.

2. Set Up the Equation:
- Let [tex]$ x $[/tex] be the number of office buildings.
- The number of windows from the office buildings is [tex]$ 21x $[/tex].
- Add the 42 windows from the school.
- The total number of cleanable windows is 126.

3. Form the Equation:
[tex]\[
21x + 42 = 126
\][/tex]

4. Solve the Equation:
- Subtract 42 from both sides to isolate terms with [tex]$ x $[/tex]:
[tex]\[
21x = 126 - 42
\][/tex]
- Simplify the right side:
[tex]\[
21x = 84
\][/tex]
- Divide both sides by 21 to solve for [tex]$ x $[/tex]:
[tex]\[
x = \frac{84}{21}
\][/tex]
- Calculate the division:
[tex]\[
x = 4
\][/tex]

This means that 4 office buildings can be washed with the available supplies. Hence, the correct equation is [tex]$ 21x + 42 = 126 $[/tex].