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
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
The equation that would be used to solve this problem algebraically is:
21x + 42 = 126
(Option 2: 21x + 42 = 126)
To solve this problem algebraically, we need to set up an equation based on the given information. Let's use the variable x to represent the number of office buildings that can be washed.
The 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 in the school is 42.
The total number of windows cleaned in both the office buildings and the school is given as 126.
So, we can set up the equation as follows:
21x + 42 = 126
The equation 21x + 42 = 126 reflects that the sum of the windows cleaned in the office buildings and the windows cleaned in the school is equal to the total number of windows cleaned.
To solve this equation, we need to isolate the variable x. We can do this by subtracting 42 from both sides of the equation:
21x + 42 - 42 = 126 - 42
21x = 84
Finally, we divide both sides of the equation by 21 to solve for x:
21x/21 = 84/21
x = 4
So, the solution is x = 4, which means that the window cleaner can wash 4 office buildings.