2025 AMC 10A Problems/Problem 2: Difference between revisions

Revision as of 15:00, 6 November 2025

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

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

@@ Line 32: / Line 32: @@
 ==See Also==
-{{AMC10 box|year=2025|ab=A|before=[[2024 AMC 10B Problems]]|after=[[2025 AMC 10B Problems]]}}
+{{AMC10 box|year=2025|ab=A|num-b=1|num-a=3}}
+{{AMC12 box|year=2025|ab=A|num-b=1|num-a=3}}
 * [[AMC 10]]
 * [[AMC 10 Problems and Solutions]]

Page

Toolbox

Search