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 minus 42 equals 126 42x−21=126 42 x minus 21 equals 126 42x+21=126 42 x plus 21 equals 126 21x+42=126
The equation that would be used to solve this problem algebraically is:
21x + 42 = 126
To solve this problem algebraically, let's assume the number of office buildings is represented by the variable x.
We know that a window cleaner can clean 21 windows per office building, so the total number of windows cleaned in the office buildings would be 21x.
Additionally, the window cleaner can clean the windows of a school with 42 windows.
Therefore, the total number of windows cleaned would be 21x + 42.
We are given that the total number of windows cleaned is 126.
So, the equation representing this situation would be: 21x + 42 = 126.
To solve for x, we need to isolate the variable. Let's rewrite the equation:
21x + 42 - 42 = 126 - 42
21x = 84
Finally, we divide both sides of the equation by 21:
21x/21 = 84/21
x = 4
Therefore, the number of office buildings that can be washed is 4.
Let's denote the number of office buildings as "x".
The supplies required to clean the 21 windows per office building would be 21x.
Since the windows of the school also need to be cleaned and there are 42 school windows, the total supplies needed would be 21x + 42.
According to the problem, the total supplies are enough to clean 126 windows.
So, the equation that represents this situation algebraically is:
21x + 42 = 126