2025 AMC 10A Problem 2

Problem 2 of 25EasierAlgebra

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?

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Solution

The starting

10

-pound mix holds

5

pounds of peanuts and

2

pounds of cashews. Add

x

pounds of the second mix, which is

20\%

peanuts. We want the new peanut fraction to be

40\%,

\frac{5 + 0.2x}{10 + x} = 0.4.

This means

5 + 0.2x = 4 + 0.4x,

giving

x = 5.

Those

5

pounds bring

0.4 \cdot 5 = 2

more pounds of cashews, so the box now has

2 + 2 = 4.

Therefore, the answer is B.