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Question

soybean mean is 14% protein; cornmeal is 7% protein. how many pounds of each should be mixed together in order to get 280-lb mixture that is 11% protein?

Answer 1

Let s

be the number of pounds of soybean meal we need for 280 lb mix;

and

let c

be the number of pounds of cornmeal we need for 280 lb mix.

We have two quantities:

Total number of pounds we know 280: it is the sum of s and c.

Equation 1: s + c = 280

We want the mix to be 11% protein.

In 280 lb we have 11% protein. It is the sum of the protein in soybean and cornmeal.

Equation 2: 14%s + 7%c = 11%x280.

We solve these two equations as a system:

s + c = 280

14s + 7c =3080

We can use substitution here:

c = 280 - s

14s + 7(280 - s) = 3080

We can make the coefficients smaller by dividing by 7:

2s + 280 - s = 440

s +280 = 440

s = 440 - 280

s =160.

Back substitution:

c = 280 - s

= 280 - 160 = 120.

We need 160 lb of soybean meal and 120 lb of cornmeal to mix 280 lb with 11% protein.

One last step you need to do: check that the step is, indeed, 11%!