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?

Answer 1

Let x = the amount of 20% protien corn meal

y = the amount of 60% feed supplement

Then

(20x + 60y)/(x + y) = 30

x + y = 3600

Solving for x & y

x = 2700 lbs (20% supplement)

y = 900 lbs (60% supplement)

Answer 2

The trick here is understanding how to work with units. And one thing about that to remember is - units cancel like fractions reduce.

Let's understand this problem in terms of units, noting we are working in pounds, since that what the problem wants:

CORN MEAL:: 20% means 20 lbs protein for every 100 lbs cornmeal,

Use a RATIO to find p, the amount of protein in C pounds of cormeal: 20/100 = p/C, p = 0.2C.

so 0.2C would be the amount of protein in C pounds of cornmeal

FEED SUPP:: 60% means 60 lbs protein for every 100 lbs feed supp,

so 0.6F would be the amount of protein in F pounds of feed supp.

WANT a mix such that you have (0.30)(3600) lbs protein when you are done mixing C pounds of cornmeal and F pounds of feed supp.

For the protein to work out, we need to add together the protein from the cornmeal and feed supp to get the amt of protein in the final mix:

0.2C + 0.6F = (0.3)(3600).

AND we know that C+F = 3600 because that's the number of pounds we want in the final mix.

Now that we thought it through - here is a recap of the final set of equations you need to solve:

C+F = 3600

0.2C + 0.6F = (0.3)(3600).

The first equation ensures you have the right pounds of mix.

The second equation ensures all the protein you get from mixing the 2 ingredients gives you 30% protein in the final mix.

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Final advice - Think your word problem through so that the units work out.