AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 4 Medium

A store purchased a batch of goods and planned to sell them at a 40\% markup. After selling 80\% of the goods at the marked-up price, the store decided to sell the remaining goods at 50\% off in order to clear the stock quickly. After all the goods were sold, the store was unexpectedly charged an additional 150 dollars tax, which caused the actual profit to be only half of the originally expected profit. What was the cost price of this batch of goods?

  • A.

    2500 dollars

  • B.

    2600 dollars

  • C.

    2700 dollars

  • D.

    2800 dollars

  • E.

    2900 dollars

Answer:A

Let the cost price be x dollars. Then the equation is:

\left(1.4x \times 0.8 + 1.4x \times 0.5 \times 0.2\right) - x - 150 = \frac{1}{2} \times 0.4x

Solving this gives: x = 2500

Answer: The cost price of the goods was 2500 dollars.