Question

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

Answer 1

To solve the problem, we can set up an equation to represent the situation.

Let:

• \( x \) be the number of office buildings that can be cleaned.

Each office building has 21 windows, so the total number of windows cleaned from all the office buildings is \( 21x \). The school has 42 windows.

According to the problem, the total number of windows cleaned (from both the office buildings and the school) is 126. Therefore, we can set up the equation as follows:

\[ 21x + 42 = 126 \]

This equation can be solved to find the value of \( x \), which represents the number of office buildings that can be washed.

Now, subtract 42 from both sides:

\[ 21x = 126 - 42 \] \[ 21x = 84 \]

Next, divide both sides by 21:

\[ x = \frac{84}{21} \] \[ x = 4 \]

So, the number of office buildings that can be washed is \( 4 \).