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
21 x plus 42 equals 126
42x+21=126
42 x plus 21 equals 126
42x−21=126
42 x minus 21 equals 126
21x−42=126
21 x minus 42 equals 126
The equation that would be used to solve this problem algebraically is:
21x + 42 = 126
To solve this problem algebraically, we can set up an equation representing the given information. Let's assume the number of office buildings is represented by 'x'.
The window cleaner can clean 21 windows per office building, so the total number of windows cleaned in the office buildings would be 21x.
The window cleaner can also clean 42 windows in the school.
And the total number of windows cleaned is 126.
Putting all this information together, we can set up the equation:
21x + 42 = 126
This equation represents the total number of windows cleaned in the office buildings (21x) plus the number of windows cleaned in the school (42), which equals the total number of windows cleaned (126).
To solve this equation, we need to isolate the variable 'x'. Here's the step-by-step process:
1. Start with the equation: 21x + 42 = 126.
2. Subtract 42 from both sides of the equation: 21x = 126 - 42.
3. Simplify the right side: 21x = 84.
4. Divide both sides of the equation by 21: x = 84 / 21.
5. Simplify the right side: x = 4.
Therefore, there are 4 office buildings that can be washed. So the equation used to solve this problem algebraically is: 21x + 42 = 126.