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| {{duplicate|[[2025 AMC 10A Problems/Problem 2|2025 AMC 10A #2]] and [[2025 AMC 12A Problems/Problem 2|2025 AMC 12A #2]]}}
| | #redirect [[2025 AMC 12A Problems/Problem 2]] |
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| ==Problem==
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| A box contains <imath>10</imath> pounds of a nut mix that is <imath>50</imath> percent peanuts, <imath>20</imath> percent cashews, and <imath>30</imath> percent almonds. A second nut mix containing <imath>20</imath> percent peanuts, <imath>40</imath> percent cashews, and <imath>40</imath> percent almonds is added to the box resulting in a new nut mix that is <imath>40</imath> percent peanuts. How many pounds of cashews are now in the box?
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| <imath>\textbf{(A) } 3.5 \qquad\textbf{(B) } 4 \qquad\textbf{(C) } 4.5 \qquad\textbf{(D) } 5 \qquad\textbf{(E) } 6</imath>
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| ==Video Solution==
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| https://youtu.be/l1RY_C20Q2M
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| ==Solution 1==
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| We are given <imath>0.2(10) = 2</imath> pounds of cashews in the first box.
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| Denote the pounds of nuts in the second nut mix as <imath>x.</imath>
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| <cmath>5 + 0.2x = 0.4(10 + x)</cmath>
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| <cmath>0.2x = 1</cmath>
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| <cmath>x = 5</cmath>
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| Thus, we have 5 pounds of the second mix.
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| <cmath>0.4(5) + 2 = 2 + 2 = \boxed{\text{(B) }4}</cmath>
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| ~pigwash
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| ~yuvaG (Formatting)
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| ==Solution 2==
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| Let the number of pounds of nuts in the second nut mix be <imath>x</imath>. Therefore, we get the equation <imath>0.5 \cdot 10 + 0.2 \cdot x = 0.4(x+10)</imath>. Solving it, we get <imath>x=5</imath>. Therefore the amount of cashews in the two bags is <imath>0.2(20%)\cdot 10 + 0.4(40%)
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| \cdot 5 = 4</imath>, so our answer choice is <imath>\boxed{\textbf{(B)} 4}</imath>.
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| ~iiiiiizh
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| ~yuvaG - <imath>\LaTeX</imath> Formatting ;)
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| ~Amon26(really minor edits)
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| ==Solution 3==
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| The percent of peanuts in the first mix is <imath>10\%</imath> away from the total percentage of peanuts, and the percent of peanuts in the second mix is <imath>20\%</imath> away from the total percentage. This means the first mix has twice as many nuts as the second mix, so the second mix has <imath>5</imath> pounds.
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| <imath>0.20 \cdot 10 + 0.40 \cdot 5 = 4</imath> pounds of cashews. So our answer is, <imath>\boxed{\textbf{(B)}4}</imath>
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| ~LUCKYOKXIAO
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| ~LEONG2023-Latex
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| ==Chinese Video Solution==
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| https://www.bilibili.com/video/BV1S52uBoE8d/
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| ~metrixgo
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| == Video Solution (Intuitive, Quick Explanation!) ==
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| https://youtu.be/Qb-9KDYDDX8
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| ~ Education, the Study of Everything
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| == Video Solution (Fast and Easy) ==
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| https://youtu.be/YpJ3QZTmDuw?si=ucvH15JKX2tw4SKZ ~ Pi Academy
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| ==Video Solution by Daily Dose of Math==
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| https://youtu.be/LN5ofIcs1kY
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| ~Thesmartgreekmathdude
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| ==Video Solution==
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| https://youtu.be/gWSZeCKrOfU
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| ~MK
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| ==See Also==
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| {{AMC10 box|year=2025|ab=A|num-b=1|num-a=3}}
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| {{AMC12 box|year=2025|ab=A|num-b=1|num-a=3}}
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| * [[AMC 10]]
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| * [[AMC 10 Problems and Solutions]]
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| * [[Mathematics competitions]]
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| * [[Mathematics competition resources]]
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| {{MAA Notice}}
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