Question

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices: The following table displays the income Jane's business earned and the percentage of that income she paid in taxes for the first half of the year. \[ \begin{array}{|c|c|c|} \hline \text{Month} & \text{Income earned ($ )} & \text{Percentage paid in taxes (%)}
\hline \text{January} & 10,000 & 10
\text{February} & 50,000 & 30
\text{March} & 20,000 & 20
\text{April} & 10,000 & 10
\text{May} & 30,000 & 20
\text{June} & 90,000 & 40
\hline \end{array} \]

• A. The average of the income tax Jane paid
• B. 22% of Jane’s average income
• C. Quantity B is greater
• D. The two quantities are equal

Hint:

To calculate averages and percentages accurately, remember to first calculate individual values before summing them up for the average.

Answer 1

The Correct Option is C

Step 1: Calculate the total tax paid by Jane.
To calculate the tax paid by Jane, we need to compute the tax paid in each month and sum them up. The tax paid in each month is: - January: \( 10,000 \times 10% = 1,000 \) - February: \( 50,000 \times 30% = 15,000 \) - March: \( 20,000 \times 20% = 4,000 \) - April: \( 10,000 \times 10% = 1,000 \) - May: \( 30,000 \times 20% = 6,000 \) - June: \( 90,000 \times 40% = 36,000 \) The total tax paid is: \[ 1,000 + 15,000 + 4,000 + 1,000 + 6,000 + 36,000 = 63,000. \]
Step 2: Find the average tax paid.
The total income earned is: \[ 10,000 + 50,000 + 20,000 + 10,000 + 30,000 + 90,000 = 210,000. \] The average tax paid is: \[ \frac{63,000}{6} = 10,500. \]
Step 3: Compare with Quantity B.
Quantity B is 22% of the average income: \[ \text{22% of 35,000} = 22% \times 35,000 = 7,700. \]
Step 4: Conclusion.
The average tax paid by Jane is 10,500, which is greater than 7,700. Hence, Quantity B is greater.