2025 AMC 10A Problems/Problem 2: Difference between revisions
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==Solution 1== | ==Solution 1== | ||
We are given <imath>0.5(10) = 5</imath> lbs of peanuts in the first box. <imath>5+0.2x = 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> | We are given <imath>0.5(10) = 5</imath> lbs of peanuts in the first box. Denote the number of nuts in the second box as x. <imath>5+0.2x = 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> | ||
~pigwash | ~pigwash | ||
==Solution 2== | ==Solution 2== | ||
Revision as of 14:07, 6 November 2025
A box contains 
pounds of a nut mix that is 
percent peanuts, 
percent cashews, and 
percent almonds. A second nut mix containing percent peanuts, 
percent cashews, and percent almonds is added to the box resulting in a new nut mix that is percent peanuts. How many pounds of cashews are now in the box?
Solution 1
We are given 
lbs of peanuts in the first box. Denote the number of nuts in the second box as x. 
so we have 
lbs of the second mix. 
~pigwash
Solution 2
Let the number of pounds in the second nut mix be 
. Therefore 
. Solving this, we get 
. Therefore the number of pounds of cashews is 
pounds 
~iiiiiizh
