Answer :
To solve this problem, we need to determine how many windows can be washed with the supplies available. Here’s a step-by-step explanation:
1. Understand the Problem:
- A window cleaner has enough supplies to clean a certain number of windows in office buildings and one school.
- The cleaner can wash 21 windows per office building.
- The school has 42 windows.
- In total, the supplies are sufficient for washing 126 windows.
2. Identify the Variables:
- Let [tex]\( x \)[/tex] be the number of office buildings.
3. Set Up the Equation:
- The total number of windows that can be cleaned is the sum of the windows in the office buildings and the windows at the school.
- For the office buildings, the cleaner can wash 21 windows per building, so for [tex]\( x \)[/tex] office buildings, the number of windows cleaned is [tex]\( 21x \)[/tex].
- The school has 42 windows.
- Therefore, the total number of windows that can be cleaned is [tex]\( 21x + 42 \)[/tex].
- We know from the problem that the total number of windows that can be washed is 126.
4. Formulate the Equation:
[tex]\[
21x + 42 = 126
\][/tex]
5. Solve the Equation:
- Subtract 42 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
21x = 126 - 42
\][/tex]
[tex]\[
21x = 84
\][/tex]
- Divide both sides by 21 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 84 \div 21
\][/tex]
[tex]\[
x = 4
\][/tex]
Thus, the window cleaner can use the supplies to wash the windows of 4 office buildings. The correct algebraic equation used to solve the problem is [tex]\( 21x + 42 = 126 \)[/tex].
1. Understand the Problem:
- A window cleaner has enough supplies to clean a certain number of windows in office buildings and one school.
- The cleaner can wash 21 windows per office building.
- The school has 42 windows.
- In total, the supplies are sufficient for washing 126 windows.
2. Identify the Variables:
- Let [tex]\( x \)[/tex] be the number of office buildings.
3. Set Up the Equation:
- The total number of windows that can be cleaned is the sum of the windows in the office buildings and the windows at the school.
- For the office buildings, the cleaner can wash 21 windows per building, so for [tex]\( x \)[/tex] office buildings, the number of windows cleaned is [tex]\( 21x \)[/tex].
- The school has 42 windows.
- Therefore, the total number of windows that can be cleaned is [tex]\( 21x + 42 \)[/tex].
- We know from the problem that the total number of windows that can be washed is 126.
4. Formulate the Equation:
[tex]\[
21x + 42 = 126
\][/tex]
5. Solve the Equation:
- Subtract 42 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
21x = 126 - 42
\][/tex]
[tex]\[
21x = 84
\][/tex]
- Divide both sides by 21 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 84 \div 21
\][/tex]
[tex]\[
x = 4
\][/tex]
Thus, the window cleaner can use the supplies to wash the windows of 4 office buildings. The correct algebraic equation used to solve the problem is [tex]\( 21x + 42 = 126 \)[/tex].
