Question

questions 9-11 refer to the following information.

automobiles sold at max car dealer, april-august

number of automobiles sold
\

$$\begin{tabular}{|l|c|} \\hline month & number \\\\ \\hline april & 275 \\\\ \\hline may & 395 \\\\ \\hline june & 405 \\\\ \\hline july & 338 \\\\ \\hline august & 262 \\\\ \\hline \\end{tabular}$$

mean price of automobiles sold
graph showing mean price of automobiles sold from april to august: april is \\$19,500, may is \\$20,000, june is \\$21,400, july is \\$20,400, august is \\$20,800

9
which of the following is closest to the mean of the prices of the 670 automobiles sold in april and may?
a) \\$19,600
b) \\$19,700
c) \\$19,800
d) \\$19,900

10
what is the percent increase of the mean price of automobiles sold from may to june?
a) 7\\%
b) 7.5\\%
c) 8\\%
d) 8.5\\%

11
max car dealer collected a tax equal to 8 percent of the price of each automobile sold in august. approximately how much did max car dealer collect in taxes from all automobiles sold in august?
a) \\$42,000
b) \\$44,000
c) \\$420,000
d) \\$440,000

Explanation:

Read data from the table and graph

We extract the sales volume and mean prices for the relevant months:

• April: Sales \(N_A = 275\), Mean Price \(P_A = \$19,500\)
• May: Sales \(N_M = 395\), Mean Price \(P_M = \$20,000\)
• June: Sales \(N_{Jn} = 405\), Mean Price \(P_{Jn} = \$21,500\)
• August: Sales \(N_{Au} = 262\), Mean Price \(P_{Au} = \$21,000\)

Calculate weighted mean for April and May

Using the Weighted Mean concept:

$$ P_{\text{mean}} = \frac{N_A \cdot P_A + N_M \cdot P_M}{N_A + N_M} $$

$$ P_{\text{mean}} = \frac{275 \cdot 19500 + 395 \cdot 20000}{670} $$

$$ P_{\text{mean}} = \frac{5,362,500 + 7,900,000}{670} = \frac{13,262,500}{670} \approx 19,794.78 $$

This is closest to \(\$19,800\) (Option C).

Calculate percent increase from May to June

Using the Percentage Word Problems knowledge point:

$$ \text{Increase} = \frac{P_{Jn} - P_M}{P_M} \times 100\% $$

$$ \text{Increase} = \frac{21500 - 20000}{20000} \times 100\% = \frac{1500}{20000} \times 100\% = 7.5\% $$

This matches Option B.

Calculate total tax collected in August

Using the Percentage Word Problems knowledge point:

• Total sales revenue in August:

$$ R = N_{Au} \cdot P_{Au} = 262 \cdot 21000 = 5,502,000 $$

• Tax collected (8 percent):

$$ T = 0.08 \cdot 5,502,000 = 440,160 $$

This is approximately \(\$440,000\) (Option D).

Answer:

Question 9

• (A) $19,600
• (B) $19,700
• (C) $19,800 (Correct answer)
• (D) $19,900

Question 10

• (A) 7%
• (B) 7.5% (Correct answer)
• (C) 8%
• (D) 8.5%

Question 11

• (A) $42,000
• (B) $44,000
• (C) $420,000
• (D) $440,000 (Correct answer)