Art of Problem Solving
Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2025 AMC 10A Problems/Problem 2

Revision as of 14:57, 6 November 2025 by Potatob01 (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?

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

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

Solution 3

The initial box has 10 pounds. With $50$ percent of it being peanuts, there are $0.5\cdot10 = 5$ pounds of peanuts.

We then add $x$ pounds of a second mix, which is $20$ percent peanuts, causing the peanuts to now be $40$ percent of the total. We write the equation \[\frac{5+0.2x}{10+x} = 0.4\] \[5+0.2x = 4+x\] \[x=5.\] This means the second mix was a total of $5$ pounds. Because $40$ percent of that is cashews, there are $0.4\cdot 5 = 2$ cashews in the second mix. The original mixture was $20$ percent cashews, so there were $0.2\cdot 10 = 2$ cashews originally. So we now have $2+2 = \boxed{4}$ cashews.

~lprado

See Also

2025 AMC 10A (Problems • Answer Key • Resources)
Preceded by
2024 AMC 10B Problems 		Followed by
2025 AMC 10B Problems
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

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

Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=2025_AMC_10A_Problems/Problem_2&oldid=265539"