Question 1097392

How many pounds of pure peanuts must be combined with a 20% peanut mix to produce 2 pounds of a 50% peanut mix?
<pre>Pure peanut is 100%
Let amount of pure peanut be P
Then amount of 20% peanut = 2 -P
We then get: 1P + .2(2 - P) = .5(2)
P + .4 - .2P = 1
.8P = 1 - .4
Amount of pure (100%) peanut, or {{{highlight_green(matrix(1,8, P, "=", .4/.8, "=", ".75,", or, 3/4, lb))}}}
As the resultant (50%) is FARTHER from pure (100%) peanut than it is to 20% peanut mix, it's expected that
the amount of 100% (pure) peanuts will be less than the amount of 20% peanut.