Calculate Percentage: Finding Occupancy Rate in 34-Story Building with 59 Filled Units

Percentage Calculations with Multi-Step Applications

What is the percentage of occupied apartments in a 34-story building if each floor has 7 apartments and a total of 59 apartments are occupied?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the percentage of occupied apartments in a 34-story building if each floor has 7 apartments and a total of 59 apartments are occupied?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Determine the total number of apartments in the building.
  • Step 2: Apply the percentage formula to find the percentage of occupied apartments.
  • Step 3: Compare the calculated percentage with the choices provided.

Now, let's work through each step:

Step 1: Calculate the total number of apartments.
The building has 34 floors and each floor has 7 apartments, so the total number of apartments is:
34×7=238 34 \times 7 = 238

Step 2: Use the percentage formula to find the occupancy rate.
The total number of occupied apartments is 59. So, the percentage of occupied apartments is calculated as:
(59238)×100 \left(\frac{59}{238}\right) \times 100

Performing the calculation, we get:
(59238)×10024.79% \left(\frac{59}{238}\right) \times 100 \approx 24.79\%

Rounding to the nearest whole number, this is approximately 25%25\%.

Step 3: Compare with choices:
The correct answer, rounding to the nearest whole number, matches choice number 2: 25%.

Therefore, the solution to the problem is 25%25\%.

3

Final Answer

25%

Key Points to Remember

Essential concepts to master this topic
  • Formula: Percentage = (part/whole) × 100 for occupancy rates
  • Technique: Calculate total first: 34 floors × 7 apartments = 238 total
  • Check: Verify 25% of 238 ≈ 59.5, which rounds to 59 ✓

Common Mistakes

Avoid these frequent errors
  • Using occupied apartments as the denominator instead of total apartments
    Don't calculate (238/59) × 100 = 403%! This gives an impossible percentage over 100% for occupancy. Always use occupied apartments as numerator and total apartments as denominator: (59/238) × 100.

Practice Quiz

Test your knowledge with interactive questions

Approximately what is \( \frac{11}{50} \) written as a percentage?

FAQ

Everything you need to know about this question

Why do I need to calculate the total apartments first?

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You need the total number of apartments as your denominator in the percentage formula. The problem gives you floors and apartments per floor, so you must multiply: 34×7=238 34 \times 7 = 238 total apartments.

Should I round my final percentage answer?

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Yes! When dealing with real-world occupancy rates, percentages are typically rounded to the nearest whole number. 24.79% 24.79\% rounds to 25%.

What if I get a decimal when calculating the total apartments?

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You won't! When counting physical objects like apartments or floors, your totals should always be whole numbers. If you get decimals, check your multiplication.

Can occupancy rate ever be over 100%?

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No! Occupancy rate represents how much of the building is filled. It can't exceed 100% because you can't have more occupied apartments than total apartments available.

How do I check if 25% is reasonable?

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Think logically: 59238 \frac{59}{238} means about 1 out of every 4 apartments is occupied. That's 25%, which makes perfect sense!

What's the difference between this and a simple fraction problem?

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This is a multi-step word problem! You must:

  • Calculate total apartments first
  • Then apply the percentage formula
  • Finally round appropriately
It's not just one calculation.

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