2025 AMC 12A 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 first box has

5

lb peanuts,

2

lb cashews, and

3

lb almonds. Adding

x

pounds of the second mix contributes

0.2x

lb peanuts and

0.4x

lb cashews. The new peanut fraction is

40\%,

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

This gives

5+0.2x=4+0.4x,

x=5.

The cashews now total

2 + 0.4(5) = 4

pounds. Thus, the correct answer is B.