SOLUTION: Soybean meal is 18% protein, cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture that is 15% protein?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Soybean meal is 18% protein, cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture that is 15% protein?      Log On


   

Question 1201152: Soybean meal is 18% protein, cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture that is 15% protein?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.
Soybean meal is 18% protein, cornmeal is 9% protein.
How many pounds of each should be mixed together in order to get 360-lb mixture that is 15% protein?
~~~~~~~~~~~~~~~~~~ 

x pounds of the 18% protein and (360-x) pounds of the 9% protein.


The protein mass equation is

    0.18x + 0.09*(360-x) = 0.15*360.


Simplify and find x

    0.18x + 0.09*360 - 0.09x = 0.15*360

    0.18x - 0.09x            = 0.15*360 - 0.09*360

        0.09x                =       21.6

            x                =       21.6/0.09 = 240.


ANSWER.  Mix 240 pounds of the soybean and 360-240 = 120 pounds of the cornmeal.

Solved.



Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
15% is closer to 18% than to 9%. Most of the mixture will be from the Soybean meal 18% protein.

360%28%2815-9%29%2F%2818-9%29%29

360%286%2F9%29

360%282%2F3%29
%282%2F3%29%28120%2B120%2B120%29

highlight%28240%29--------pounds of the Soybean, 18% protein
and
highlight%28120%29--------pounds of the cornmeal, 9% protein

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


If the speed of finding the answer is important and formal algebra is not required (as in a timed math competition), here is a quick and easy way to solve any 2-part "mixture" problem like this.

15% is 2/3 of the way from 9% to 18% (picture the three percentages on a number line, if it helps)
That means 2/3 of the mixture is the higher percentage ingredient.

ANSWER: 2/3 of 360 pounds, or 240 pounds, of the 18% protein ingredient; the other 120 pounds of the 9%.

CHECK:
240(.18)+120(.09) = 43.2+10.8 = 54
360(.15) = 54