Question

A new apartment complex purchased 60 toilets and 20 shower heads. If the price of a toilet is three times the price of a shower head, what percent of the total cost was the cost of all the shower heads?

• A. 9%
• B. 10%
• C. 11%
• D. 13%
• E. 15%

Hint:

In problems where prices or quantities are relative, you don't need the actual price. You can assign a simple variable (like 'x') or even a simple number (like $1) to the base item. The relationships will hold, and the unknown variable will cancel out in the final percentage calculation.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem asks for the percentage contribution of one part (the cost of shower heads) to the whole (the total cost of all items). This requires setting up algebraic expressions for the costs based on the given price relationship.
Step 2: Detailed Explanation:
Part 1: Define variables for the prices
Let \( P_S \) be the price of one shower head.
Let \( P_T \) be the price of one toilet.
From the problem statement, "the price of a toilet is three times the price of a shower head":
\[ P_T = 3 \times P_S \] Part 2: Calculate the total cost of each type of item
- Number of shower heads = 20.
Total cost of shower heads = \( 20 \times P_S \).
- Number of toilets = 60.
Total cost of toilets = \( 60 \times P_T \). Substitute the price relationship from Part 1:
Total cost of toilets = \( 60 \times (3 \times P_S) = 180 \times P_S \). Part 3: Calculate the total cost of the entire purchase
\[ \text{Total Cost} = (\text{Total cost of shower heads}) + (\text{Total cost of toilets}) \] \[ \text{Total Cost} = (20 \times P_S) + (180 \times P_S) = 200 \times P_S \] Part 4: Calculate the required percentage
The question asks what percent of the total cost was the cost of all shower heads.
\[ \text{Percentage} = \frac{\text{Total cost of shower heads}}{\text{Total Cost}} \times 100% \] \[ \text{Percentage} = \frac{20 \times P_S}{200 \times P_S} \times 100% \] The variable \( P_S \) cancels out.
\[ \text{Percentage} = \frac{20}{200} \times 100% = \frac{1}{10} \times 100% = 10% \] Step 3: Final Answer
The cost of all the shower heads was 10% of the total cost.