AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 5 Medium

A shop goes to the apple-producing area to purchase apples at a cost of 1.2 dollars per kilogram. The distance from the production site to the shop is 400\,\text{km}, and the transportation fee is 1.5 dollars per ton per kilometer. If there is a 10\% loss during transportation and sales, and the shop wants to earn a profit of 15\% based on the purchase cost of the apples, what should the retail price be per kilogram?

  • A.

    2 dollars

  • B.

    2.1 dollars

  • C.

    2.2 dollars

  • D.

    2.3 dollars

  • E.

    2.4 dollars

Answer:D

Assume the shop purchases 1 ton of apples, and 1 ton = 1000 kilograms.

1000 \times 1.2 + 1 \times 1.5 \times 400 = 1200 + 600 = 1800 \quad \text{(dollars)} \quad \text{<total cost>}

1000 \times (1 - 10\%) = 1000 \times 90\% = 900 \quad \text{(kilograms)} \quad \text{<actual quantity sold>}

1800 \div 900 = 2 \quad \text{(dollars)} \quad \text{<cost per kilogram>}

2 \times (1 + 15\%) = 2 \times 115\% = 2.3 \quad \text{(dollars)} \quad \text{<retail price per kilogram>}

Related Problems
Problem 3 AMC 8 Daily Practice Round 8
Problem 4 AMC 8 Daily Practice Round 8
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