2025 AMC 10A Problems/Problem 2: Difference between revisions
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==Solution 1== | ==Solution 1== | ||
We are given <imath>0.2(10) = 2</imath> | We are given <imath>0.2(10) = 2</imath> pounds of cashews in the first box. | ||
Denote the pounds of nuts in the second nut mix as <imath>x.</imath> | |||
<cmath>5 + 0.2x = 0.4(10 + x)</cmath> | |||
<cmath>0.2x = 1</cmath> | |||
<cmath>x = 5</cmath> | |||
Thus, we have 5 pounds of the second mix. | |||
<cmath>0.4(5) + 2 = 2 + 2 = \boxed{\text{(B) }4}</cmath> | |||
~pigwash | ~pigwash | ||
Revision as of 19:57, 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
TOOO EZ
Solution 1
We are given 
pounds of cashews in the first box.
Denote the pounds of nuts in the second nut mix as 
![\[5 + 0.2x = 0.4(10 + x)\]](http://latex-new.aopstest.com/4/6/5/465abe12e05bb15bc19b04d9c82116ed04c90e91.png)
![\[0.2x = 1\]](http://latex-new.aopstest.com/c/4/a/c4afc4b51c5f6fa0f9bf78a34e438ededa7fd19e.png)
![\[x = 5\]](http://latex-new.aopstest.com/6/7/7/6773f565392dfa07209879afbc209b09615f5048.png)
Thus, we have 5 pounds of the second mix.
![\[0.4(5) + 2 = 2 + 2 = \boxed{\text{(B) }4}\]](http://latex-new.aopstest.com/b/4/3/b43ffd87b3276968f1dad2a69b98033075c839d7.png)
~pigwash
Solution 2
Let the number of pounds of nuts in the second nut mix be 
. Therefore, we get the equation 
. Solving it, we get 
. Therefore the amount of cashews in the two bags is 
, so out answer choice is 
.
~iiiiiizh
~yuvaG - 
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.
pounds of cashews. So our answer is, 
~LUCKYOKXIAO
Video Solution (Intuitive, Quick Explanation!)
~ 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
~Thesmartgreekmathdude
Video Solution
~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. 
