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)
Let x be the number of office buildings.
The number of windows in the office buildings is 21x.
The equation representing the total number of windows that can be cleaned is 21x + 42 = 126.
To solve this algebraically, one would set up the equation 21x + 42 = 126 and solve for x.
Let's represent the number of office buildings as 'x'.
Since a window cleaner can clean 21 windows per office building, the number of windows in the office buildings would be 21x.
We also know that there are 42 windows in the school.
Therefore, the total number of windows to be cleaned is 21x + 42.
According to the problem, the total number of windows to be cleaned is 126.
So, we can set up the equation: 21x + 42 = 126.
This equation can be used to solve for the number of office buildings algebraically.
To solve this problem algebraically, let's define the following:
Let x = number of office buildings.
Let y = number of windows cleaned per office building.
From the given information, we can create the following equations:
1. The number of windows cleaned per office building: x * y = 21x.
2. The number of windows cleaned in the school: 42.
3. The total number of windows cleaned: 21x + 42 = 126.
To find the number of office buildings, we can solve equation 3 for x:
21x + 42 = 126
21x = 126 - 42
21x = 84
x = 84 / 21
x = 4
Therefore, the solution is x = 4, indicating that there are 4 office buildings that can be washed.