SOLUTION: 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 shoul

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Question 1203078: 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?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Mix 20% and 10% to have 1200 pounds of 15%;
That's reaching halfway between.
600 of EACH!

Some arithmetic to help,
x of the 20% protein
1200-x of the 10% protein
20x%2B10%281200-x%29=15%2A1200

20x-10x%2B10%2A1200=15%2A1200
%2820-10%29x=15%2A1200-10%2A1200
x=1200%28%2815-10%29%2F%2820-10%29%29
x=1200%285%2F10%29
x=1200%281%2F2%29
x=600----------------you finish.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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?
~~~~~~~~~~~~~~~~ 

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.