2025 AMC 10A Problems/Problem 2

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

We are given $0.5(10) = 5$ lbs of peanuts in the first box. Denote the number of nuts in the second box as $x$ . $5+0.2x = 0.4(10+x), 0.2x = 1, x = 5$ so we have $5$ lbs of the second mix. $0.4(5)+2 = 2+2 = \boxed{\text{(B) }4}.$

~pigwash

Solution 2

Let the number of pounds in the second nut mix be $x$ . Therefore $0.5 * 10 + 0.2 * x = 0.4 * (10+x)$ . Solving this, we get $x = 5$ . Therefore the number of pounds of cashews is $0.2 * 10 + 0.4 * 5 = 4$ pounds $=>$ $\boxed{\text{(B) }4}.$

~iiiiiizh

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2025 AMC 10A Problems/Problem 2

Solution 1

Solution 2