2025 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 2 Easy

A box contains 10 pounds of a nut mix that is 50 percent peanuts, 20 percent cashews, and 30 percent almonds. A second nut mix containing 20 percent peanuts, 40 percent cashews, and 40 percent almonds is added to the box resulting in a new nut mix that is 40 percent peanuts. How many pounds of cashews are now in the box?

  • A.

    3.5

  • B.

    4

  • C.

    4.5

  • D.

    5

  • E.

    6

Answer:B

Define x as the weight (in pounds) of the second mixture.

The proportion of peanuts in the combined mixture satisfies: \frac{0.2x + 10 \times 0.5}{x + 10} = 0.4 \Rightarrow 5 + 0.2x = 4 + 0.4x, \quad 0.2x = 1, \quad x = 5. Therefore, the cashew content equals 10 \times 0.2 + 5 \times 0.4 = 4 pounds.

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