SOLUTION: A corn meal feed is 20% protein and a feed supplement is 60% protein. How much of each must be combined to get 3600 pounds of deed that is 30% protein?

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Question 1143970: A corn meal feed is 20% protein and a feed supplement is 60% protein. How much of each must be combined to get 3600 pounds of deed that is 30% protein?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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..., feed is 20% protein and a feed supplement is 60% protein. How much of each must be combined to get 3600 pounds of feed that is 30% protein?
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x, amount of the 60% protein feed
3600-x, amount of the 20% protein feed

60x%2B20%282600-x%29=30%2A3600
Simplify and solve.

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the amount (in pounds) of the 20% protein corn meal,  and 

let y be the amount of the feed supplement of 60% protein.


Then from the condition you have these two equations


        x +     y = 3600      pounds  combined   (1)

    0.20x + 0.60y = 0.3*3600  pounds  protein    (2)


To solve this system of two equations, first simplify equation (2) (right side).

Then from equation (1) express x = 3600 - y  and substitute it into equation (2). You will get one single equation for y


    0.20*(3600-y) + 0.60y = 1080,

    0.20*3600 - 0.2y + 0.6y = 1080

    0.4y                    = 1080 - 0.2*3600

       y                    = %281080-0.2%2A3600%29%2F0.4 = 900.


ANSWER.  900 pounds of the 60% feed supplement should be combined with  3600-900 = 2700 pounds of the 20% corn meal.


CHECK.  %280.2%2A2700%2B0.6%2A900%29%2F3600 = 0.3 = 30% of the resulting protein concentration feed.    ! Correct !


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It is a typical mixture problem.

There is entire bunch of lessons covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
    - Word problems on mixtures for dry substances like soil and sand
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - OVERVIEW of lessons on word problems for mixtures
in this site.

A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

Read them and become an expert in solution the mixture word problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Mixture problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Other tutors have shown two standard algebraic solution methods for solving this kind of problem, one using two variables and one using a single variable.

Here is a non-algebraic method for solving mixture problems that will get you to the answer with just a few simple calculations. If the numbers are "nice", as in this example, you can probably do the calculations mentally.

Here are the two simple steps for this method of solving this problem.

(1) 30% is 1/4 of the way from 20% to 60%. (Imagine the three percentages -- 20, 30, and 60 -- on a number line; 30 is 1/4 of the way from 20 to 60.)

(2) That means 1/4 of the mixture must be the feed supplement with 60% protein.

ANSWER: 1/4 of 3600 pounds = 900 pounds of the 60% protein feed supplement; the remaining 2700 pounds of the 20% corn meal feed.