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2025 AMC 10A Problems/Problem 2

Revision as of 01:41, 7 November 2025 by Metrixgo (talk | contribs)
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?

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

Video Solution

https://youtu.be/l1RY_C20Q2M

Solution 1

We are given $0.2(10) = 2$ pounds of cashews in the first box.

Denote the pounds of nuts in the second nut mix as $x.$

\[5 + 0.2x = 0.4(10 + x)\] \[0.2x = 1\] \[x = 5\]

Thus, we have 5 pounds of the second mix.

\[0.4(5) + 2 = 2 + 2 = \boxed{\text{(B) }4}\]


~pigwash

~yuvaG (Formatting)

Solution 2

Let the number of pounds of nuts in the second nut mix be $x$. Therefore, we get the equation $0.5 \cdot 10 + 0.2 \cdot x = 0.4(x+10)$. Solving it, we get $x=5$. Therefore the amount of cashews in the two bags is $0.2 \cdot 10 + 0.4 \cdot 5 = 4$, so our answer choice is $\boxed{\textbf{(B)} 4}$.

~iiiiiizh

~yuvaG - $\LaTeX$ Formatting ;)

~Amon26(really minor formatting)

Solution 3

The percent of peanuts in the first mix is $10\%$ away from the total percentage of peanuts, and the percent of peanuts in the second mix is $20\%$ away from the total percentage. This means the first mix has twice as many nuts as the second mix, so the second mix has $5$ pounds. $0.20 \cdot 10 + 0.40 \cdot 5 = 4$ pounds of cashews. So our answer is, $\boxed{\textbf{(B)}4}$

~LUCKYOKXIAO ~LEONG2023-Latex

Chinese Video Solution

https://www.bilibili.com/video/BV1S52uBoE8d/

~metrixgo

Video Solution (Intuitive, Quick Explanation!)

https://youtu.be/Qb-9KDYDDX8

~ Education, the Study of Everything

Video Solution (Fast and Easy)

https://youtu.be/YpJ3QZTmDuw?si=ucvH15JKX2tw4SKZ ~ Pi Academy

Video Solution by Daily Dose of Math

https://youtu.be/LN5ofIcs1kY

~Thesmartgreekmathdude

Video Solution

https://youtu.be/gWSZeCKrOfU

~MK

See Also

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

These problems are copyrighted © by the Mathematical Association of America.

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