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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?
| | #redirect [[2025 AMC 12A Problems/Problem 2]] |
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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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| ==Solution 1==
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| We are given <imath>0.5(10) = 5</imath> lbs of peanuts in the first box. <imath>5+0.2(x) = 0.4(10+x), 0.2x = 1, x = 5</imath> so we have <imath>5</imath> lbs of the second mix. <imath>0.4(5)+2 = 2+2 = \boxed{\text{(B) }4}.</imath>
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| ~pigwash
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| We have <imath>5</imath> pounds of peanuts, <imath>2</imath> pounds of cashews, and <imath>3</imath> pounds of almonds in the first nut mix.
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| Let there be <imath>x</imath> pounds of nuts in the second nut mix, thus we have <imath>0.2x</imath> worth of peanuts. That means:
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| <imath>\( \frac{5 + 0.2x}{10 + x} = 0.4 \)</imath>
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| <imath>5+0.2x=0.4(10+x)
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| 5+0.2x=4+0.4x
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| 1=0.2x
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| x=5</imath>
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| That means we have 5 pounds of the second nut mix. We are trying to find the amount of cashews in pounds.
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| <imath>10*0.2+5*0.4=2+2=4</imath>
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| There are a total of <cmath>\fbox{\textbf{(B)} 4}</cmath>
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