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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. $5+0.2(x) = 0.4(10+x), 0.2x = 1, x = 5$ so we have $5$ lbs of the second mix. $0.4(5)+2 = 2+2 = \boxed{\text{(B) }4}.$

~pigwash



We have $5$ pounds of peanuts, $2$ pounds of cashews, and $3$ pounds of almonds in the first nut mix.

Let there be $x$ pounds of nuts in the second nut mix, thus we have $0.2x$ worth of peanuts. That means:

$( \frac{5 + 0.2x}{10 + x} = 0.4 \)$ (Error compiling LaTeX. Unknown error_msg)

$5+0.2x=0.4(10+x) 5+0.2x=4+0.4x 1=0.2x x=5$

That means we have 5 pounds of the second nut mix. We are trying to find the amount of cashews in pounds.


$10*0.2+5*0.4=2+2=4$


There are a total of \[\fbox{\textbf{(B)} 4}\]

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