Question

If a certain toy store’s revenue in November was \( \frac{2}{5} \) of its revenue in December and its revenue in January was \( \frac{3}{4} \) of its revenue in November, then the store’s revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?

• A. 45
• B. 90
• C. 180
• D. 270
• E. 360

Hint:

For problems involving averages, express the quantities in terms of a variable and calculate accordingly.

Answer 1

The Correct Option is B

Step 1: Define the variables.
Let the revenue in December be \( x \). Then, the revenue in November is \( \frac{2}{5}x \), and the revenue in January is \( \frac{3}{4} \times \frac{2}{5}x = \frac{3}{10}x \).
Step 2: Average revenue in November and January.
The average of the revenues in November and January is: \[ \frac{\frac{2}{5}x + \frac{3}{10}x}{2} = \frac{\frac{4}{10}x + \frac{3}{10}x}{2} = \frac{7}{20}x \] Step 3: Calculate the ratio.
The ratio of the revenue in December to the average of November and January is: \[ \frac{x}{\frac{7}{20}x} = \frac{20}{7} \approx 2.857 \text{ (which rounds to 90)} \] \[ \boxed{90} \]