2025 AMC 10A Problems/Problem 2

The following problem is from both the 2025 AMC 10A #2 and 2025 AMC 12A #2, so both problems redirect to this page.

Problem

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?

$\textbf{(A)}~3.5\qquad\textbf{(B)}~4\qquad\textbf{(C)}~4.5\qquad\textbf{(D)}~5\qquad\textbf{(E)}~6$

Solution 1

Since the first box had 5 pounds, and 50 percent of it had peanuts, we know there were 5 pounds of peanuts at the beginning.

Adding the second mixture of nuts, we call this value $x$ , as in $x$ pounds. Of that, 20%, or $\frac{x}{5}$ , are peanuts.

Since the final percentage is 40 percent peanuts, we have $\frac{5 + \frac{x}{5}}{10 + x} = \frac{2}{5}.$

Multiplying both sides by $5(10 + x)$ , we get $25 + x = 20 + 2x.$

This gives us $x = 5$ .

But the problem is asking us to solve for cashews.

The first mixture was $\frac{1}{5}$ cashews, so there were $2$ pounds of cashews in the first mix. In the second, there were $\frac{2x}{5}$ cashews, or 2 pounds of cashews.

Adding this together gives us a final total of $2 + 2 = \boxed{4}$ pounds of cashews.

~Minor edits to LaTeX by WildSealVM/Vincent M

2025 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

2025 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

Page

Toolbox

Search

2025 AMC 10A Problems/Problem 2

Problem

Solution 1

See Also