Question

A bicycle registration costs \(\$2.250\) in City X and \(\$3.00\) in City Y. At these rates, the cost of 4 registrations in City X is k percent of the cost of 3 registrations in City Y.
Column A: k
Column B: 90

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

Break down word problems into smaller steps: 1. Identify the values you need to calculate (Cost A and Cost B). 2. Perform the calculations. 3. Set up the final equation based on the question (in this case, the percent formula) and solve.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a word problem that requires calculating total costs and then finding a percentage relationship between them.
Step 2: Key Formula or Approach:
The statement "A is P percent of B" translates to the equation \( A = \frac{P}{100} \times B \). We need to calculate the values for A and B first, then solve for P (which is \(k\) in this problem).
Step 3: Detailed Explanation:
First, calculate the two total costs.
Cost in City X (A): Cost of 4 registrations at $2.25 each.
\[ A = 4 \times $2.25 = $9.00 \] Cost in City Y (B): Cost of 3 registrations at $3.00 each.
\[ B = 3 \times $3.00 = $9.00 \] Now, we are told that the cost in City X is \(k\) percent of the cost in City Y. So, A is \(k\) percent of B.
\[ 9.00 = \frac{k}{100} \times 9.00 \] To solve for \(k\), we can divide both sides by 9.00:
\[ 1 = \frac{k}{100} \] Multiply both sides by 100:
\[ k = 100 \] So, the value of \(k\) in Column A is 100.
Comparison: Column A: \( k = 100 \).
Column B: 90.
Since \( 100>90 \), the quantity in Column A is greater.
Step 4: Final Answer:
The value of k is 100, which is greater than 90.