Multiple choice

A shopkeeper made the payment of \$150 for a shipment of n identical Christmas gifts. He kept one gift for his friend and sold each of the others for \$5 more than the average cost of n gifts. The total revenue from the sale of the gifts was $60 more than the cost of the shipment. Quantity A Number of gifts sold Quantity B 15

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cost per gift = 150/n. Selling price = (150/n) + 5. Total revenue = (n-1)(150/n + 5) = 150 + 5n - 150/n - 5 = 145 + 5n - 150/n. Revenue = Cost + 60 = 150 + 60 = 210. So, 145 + 5n - 150/n = 210, 5n - 150/n = 65, n^2 - 13n - 30 = 0. Solving (n-15)(n+2) = 0 gives n = 15. Number of gifts sold is n-1 = 14. Quantity A (14) < Quantity B (15).

AI explanation

The average cost of the n gifts is 150 divided by n dollars. The shopkeeper sells n minus 1 gifts at a price of 5 plus 150 divided by n, generating a total extra revenue of 60 dollars over the cost. Multiplying the number of sold gifts by the extra revenue per gift gives the equation n minus 1 multiplied by 5 equals 60. Solving this gives n minus 1 equals 12, meaning 12 gifts were sold. Comparing this to Quantity B, 15 is greater than 12, so Quantity B is greater.

Keep practicing — related questions