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| ==Problem== | | ==Problem== |
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| == Solution 1==
| | #redirect[[2025 AMC 10A Problems/Problem 1]] |
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| The initial box has 10 pounds. With <imath>50</imath> percent of it being peanuts, there are <imath>0.5\cdot10 = 5</imath> pounds of peanuts.
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| We then add <imath>x</imath> pounds of a second mix, which is <imath>20</imath> percent peanuts, causing the peanuts to now be <imath>40</imath> percent of the total. We write the equation
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| <cmath>\frac{5+0.2x}{10+x} = 0.4</cmath>
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| <cmath>5+0.2x = 4+x</cmath>
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| <cmath>x=5.</cmath>
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| This means the second mix was a total of <imath>5</imath> pounds. Because <imath>40</imath> percent of that is cashews, there are <imath>0.4\cdot 5 = 2</imath> cashews in the second mix. The original mixture was <imath>20</imath> percent cashews, so there were <imath>0.2\cdot 10 = 2</imath> cashews originally. So we now have <imath>2+2 = \boxed{4}</imath> cashews.
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| ~lprado
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