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Answer :
To solve this problem, we need to determine how many office buildings can be washed with the available supplies. Here's how you can think through it step by step:
1. Understand the Problem:
- We know the window cleaner can clean 21 windows per office building.
- There's also a school that has 42 windows.
- Altogether, there are supplies to clean 126 windows in total.
2. Define the Variables:
- Let [tex]\( x \)[/tex] represent the number of office buildings.
3. Set Up the Equation:
- The windows in the office buildings can be represented as [tex]\( 21x \)[/tex] because each building has 21 windows and there are [tex]\( x \)[/tex] buildings.
- Adding the school windows, the total number of windows the cleaner can handle is represented by [tex]\( 21x + 42 \)[/tex].
- This total is given to be 126 windows. So, we set up the equation:
[tex]\[
21x + 42 = 126
\][/tex]
4. Solve the Equation:
- First, subtract 42 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
21x = 126 - 42
\][/tex]
[tex]\[
21x = 84
\][/tex]
- Next, divide both sides by 21 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{84}{21}
\][/tex]
[tex]\[
x = 4
\][/tex]
5. Conclusion:
- The window cleaner can wash the windows for 4 office buildings.
So, the equation you would use to solve this problem is [tex]\( 21x + 42 = 126 \)[/tex], making option [tex]\( 21x + 42 = 126 \)[/tex] the correct choice.
1. Understand the Problem:
- We know the window cleaner can clean 21 windows per office building.
- There's also a school that has 42 windows.
- Altogether, there are supplies to clean 126 windows in total.
2. Define the Variables:
- Let [tex]\( x \)[/tex] represent the number of office buildings.
3. Set Up the Equation:
- The windows in the office buildings can be represented as [tex]\( 21x \)[/tex] because each building has 21 windows and there are [tex]\( x \)[/tex] buildings.
- Adding the school windows, the total number of windows the cleaner can handle is represented by [tex]\( 21x + 42 \)[/tex].
- This total is given to be 126 windows. So, we set up the equation:
[tex]\[
21x + 42 = 126
\][/tex]
4. Solve the Equation:
- First, subtract 42 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
21x = 126 - 42
\][/tex]
[tex]\[
21x = 84
\][/tex]
- Next, divide both sides by 21 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{84}{21}
\][/tex]
[tex]\[
x = 4
\][/tex]
5. Conclusion:
- The window cleaner can wash the windows for 4 office buildings.
So, the equation you would use to solve this problem is [tex]\( 21x + 42 = 126 \)[/tex], making option [tex]\( 21x + 42 = 126 \)[/tex] the correct choice.
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