SOLUTION: A dairy farmer wants to mix a 45% protein supplement and a standard 20% protein ration to make 2000 pounds of a high-grade 35% protein ration. How many pounds of each shoul

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Question 1201992: A dairy farmer wants to mix a 45%
protein supplement and a standard 20%
protein ration to make 2000
pounds of a high-grade 35%
protein ration. How many pounds of each should he use?
Found 3 solutions by mananth, josgarithmetic, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
A dairy farmer wants to mix a 45%
protein supplement and a standard 20%
protein ration to make 2000
pounds of a high-grade 35%
protein ration. How many pounds of each should he use?
component percent ---------------- quantity
Protein A 0.45 ---------------- x lbs
Protein B 0.2 ---------------- 2000 - x lbs
Mixture 0.35 ---------------- 2000

0.45 x + 0.2 ( 2000 - x ) = 2000.00 * 0.35

0.45 x + 400 - 0.2 x = 700.00
0.45 x - 0.2 x = 700 - 400
0.25 x = 300
/ 0.25
x = 1200 lbs 45.00% Protein A
800 lbs 20.00% Protein B

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
45% protein and 20% protein
to make 2000 pounds of 35% 
PERCENTAGE
SUPPLEMENT        QUANTITY      PROTEIN
   45                h            45h
   20               2000-h       20(2000-h)
-----------------------------------------
   35              2000         35*2000

highlight_green%2845h%2B20%282000-h%29=35%2A2000%29
45h-20h%2B20%2A2000=35%2A2000
%2845-20%29h=35%2A2000-20%2A2000
highlight%28h=%282000%2835-20%29%29%2F%2845-20%29%29-----simplify, compute, and finish.
-

h=2000%28%2835-20%29%2F%2845-20%29%29
h=2000%2815%2F25%29
h=2000%283%2F5%29
h=%28100%2A4%2A5%2A3%29%2F5
highlight%28h=1200%29

1200 pounds the 45%
800 pounds of the 20%

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


Presumably this problem is to be solved using formal algebra. If so, then use the standard solution method shown by the other tutors.

If formal algebra is not required, here is a quick and easy informal way to solve any 2-part mixture problem like this.

The mixture's percentage of 35% is 15/25 = 3/5 of the way from 20% to 45% (look at the numbers 20, 35, and 45 on a number line to see this, if it helps).

That means 3/5 of the mixture is the higher percentage ingredient.

3/5 of 2000 pounds is 1200 pounds.

So...

ANSWER: 1200 pounds of the 45% protein, 800 pounds of the 20% protein.

CHECK:
.45(1200) + .20(800) = 540 + 160 = 700
.35(2000) = 700