A dairy farmer wants to mix a 20% protein supplement
and a standard 10% protein ration
to make 1200 pounds of a high-grade 15%
protein ration. How many pounds of each should he use?
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x pounds of the 20% protein supplement and
(1200-x) pounds of a standard 10% protein ration.
The protein total mass equation is
0.2x + 0.10*(1200-x) = 0.15*1200
Simplify, solve and find x
0.2x + 120 - 0.1x = 180
0.2x - 0.1x = 180 - 120
0.1x = 60
x = 60/0.1 = 600.
ANSWER. 600 pounds of the 20% protein supplement and 1200-600 = 600 pounds of the standard 10% protein ration.
Solved.
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It also can be solved MENTALLY (~ guessed from the first glance), if to notice that
15% of the resulting protein concentration is half-way between 10% and 20% of the
input ingredients.