Problem:
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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the weight of the second mix be pounds.
We start by finding the equation for the number of peanuts. We get
Therefore, in the final mixture of pounds, we know that peanuts are of the mixture, so we can setup the following equation to get:
We can solve the equation to get .
Now, let's find the number of cashews in the final mixture. We know
so the final mixture contains pounds of cashews, for an answer of .
The problems on this page are the property of the MAA's American Mathematics Competitions