SOLUTION: How many pounds of a chicken feed that is 45% corn must be mixed with 480 lb of a feed that is 80% corn to make a chicken feed that is 75% corn?

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Question 1189766: How many pounds of a chicken feed that is 45% corn must be mixed with 480 lb of a feed that is 80% corn to make a chicken feed that is 75% corn?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
How many pounds of a chicken feed that is 45% corn must be mixed
with 480 lb of a feed that is 80% corn to make a chicken feed that is 75% corn?
~~~~~~~~~~~~~~~~ 

Let x be the unknown value under the problem's question.


Then you have this balance equation for the corn content

    0.45x + 0.80*480 = 0.75*(480+x).


From the equation

    x =  = 80.


ANSWER.  80 pounds should be added.

CHECK.   80*0.45 + 480*0.8 = 420 pounds of corn, the same as (80+480)*0.75, which proves the correctness.

Solved.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


The solution from the other tutor is a fine formal algebraic way to solve the problem; and it is probably the "standard" formal algebraic method.

Here are a couple of versions of a non-algebraic way to solve any 2-part "mixture" problem like this.

(1) Look at the percentages of the two ingredients and the mixture on a number line -- 45, 75, and 80 -- and observe/calculate that 75 is 30/35 = 6/7 of the way from 45 to 80. That means 6/7 of the mixture is the ingredient that is 80% corn.

That means the ingredient that is 45% corn is 1/7 of the mixture -- which is 1/6 as much as the 80% corn. Then, since there are 480lb of the 80% corn, the number of pounds of 45% corn is 480/6 = 80.

ANSWER: 80 lb

(2) The same concept, using slightly different reasoning and so different calculations....

80-75=5; 75-45=30.
5 is 1/6 as much as 30.
So the amount of 45% corn should be 1/6 the amount of 80% corn.
ANSWER: 1/6 of 480 lb, or 80 lb
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