Questions: Twenty people want to sell their cars. The amounts they will accept are summarized in the list below. 800, 1,000, 1,200, 1,500, 1,800, 2,000, 2,100, 2,400, 2,500, 2,750, 3,000, 3,300, 3,500, 3,750, 4,000, 4,250, 4,500, 4,900, 5,000, 5,300 The percentage of lemons, or cars valued at 2,250 or less, is 35% in this offering of cars. If the market has a realistic estimate of the number of lemons, the market values quality cars at 4,300, and those sellers who cannot expect a price buyers are willing to pay will give their cars to family members instead of offering them for sale, what percentage of the cars actually offered for sale will be lemons? 34% 66% 35% 44%

Twenty people want to sell their cars. The amounts they will accept are summarized in the list below. 800, 1,000, 1,200, 1,500, 1,800, 2,000, 2,100, 2,400, 2,500, 2,750, 3,000, 3,300, 3,500, 3,750, 4,000, 4,250, 4,500, 4,900, 5,000, 5,300
The percentage of lemons, or cars valued at 2,250 or less, is 35% in this offering of cars. If the market has a realistic estimate of the number of lemons, the market values quality cars at 4,300, and those sellers who cannot expect a price buyers are willing to pay will give their cars to family members instead of offering them for sale, what percentage of the cars actually offered for sale will be lemons?
34%
66%
35%
44%

Transcript text: Twenty people want to sell their cars. The amounts they will accept are summarized in the list below. $\$ 800, \$ 1,000, \$ 1,200, \$ 1,500, \$ 1,800, \$ 2,000, \$ 2,100, \$ 2,400, \$ 2,500, \$ 2,750, \$ 3,000, \$ 3,300, \$ 3,500, \$ 3,750$, $\$ 4,000, \$ 4,250, \$ 4,500, \$ 4,900, \$ 5,000, \$ 5,300$ The percentage of lemons, or cars valued at $\$ 2,250$ or less, is $35 \%$ in this offering of cars. If the market has a realistic estimate of the number of lemons, the market values quality cars at $\$ 4,300$, and those sellers who cannot expect a price buyers are willing to pay will give their cars to family members instead of offering them for sale, what percentage of the cars actually offered for sale will be lemons? 34\% 66\% 35\% 44\%

Solution

Solution Steps

To determine the percentage of cars actually offered for sale that are lemons, we need to first identify which cars are considered lemons (valued at $2,250 or less) and which are quality cars (valued above $2,250). Given that the market values quality cars at $4,300, we need to find out how many cars are valued above this amount and will be offered for sale. Then, we calculate the percentage of lemons among the cars that are actually offered for sale.

Step 1: Identify Lemons

We define lemons as cars valued at $ \leq 2250 $. From the list of car prices, we find that there are 7 lemons.

Step 2: Identify Quality Cars Offered

Quality cars are those valued at $ > 4300 $. From the list, we find that there are 4 quality cars that will be offered for sale.

Step 3: Calculate Total Cars Offered for Sale

The total number of cars offered for sale is the sum of lemons and quality cars: \[ \text{Total Offered for Sale} = \text{Lemons} + \text{Quality Cars Offered} = 7 + 4 = 11 \]

Step 4: Calculate Percentage of Lemons Offered

The percentage of lemons among the cars offered for sale is calculated as follows: \[ \text{Percentage of Lemons Offered} = \left( \frac{\text{Lemons}}{\text{Total Offered for Sale}} \right) \times 100 = \left( \frac{7}{11} \right) \times 100 \approx 63.64 \]