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.(1 point)
Responses
21x+42=126
42x−21=126
42x+21=126
21x−42=126
The correct equation to represent this situation is:
21x + 42 = 126
Here's the breakdown of the equation:
- Let x be the number of office buildings that can be cleaned.
- Each office building requires enough supplies to clean 21 windows, so for x buildings you will need 21x supplies.
- There is also one school with 42 windows that will be cleaned, represented by the "+ 42".
- Altogether, there are enough supplies to clean 126 windows, represented by "= 126" on the other side of the equation.
Now, we need to solve this equation for x:
21x + 42 = 126
Subtract 42 from both sides to isolate the term with x:
21x = 126 - 42
21x = 84
Now, divide both sides by 21 to solve for x:
x = 84 / 21
x = 4
Therefore, the window cleaner has enough supplies to wash the windows of 4 office buildings.