Soybean meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240lb mixture that is 7% protein?

Question

how many pounds of cornmeal and soybeans should there be in the mixture?

Answer 1

Hello Mackie,

 

Because you do not know how many lbs of soybean meal and cornmeal you need to mix together, you should label these as x and y respectively:

Pounds of Soybean Meal = x

Pounds of Cornmeal = y

 

From the word problem, there are two equations that can be written. The first equation can be written from this part of the word problem:

"How many pounds of each should be mixed together in order to get 240lb mixture..."

From this you can safely assume that mixing is addition, and because we assigned x and y to the two protein sources, an equation can be written as follows:

x+y=240

 

The second equation can be written from the following:

"Soybean meal is 12% protein; cornmeal is 6% protein...in order to get 240lb mixture that is 7% protein?"

This means that the mass of soybean meal that is protein is 12% of the total mass of soybean meal or 0.12*x.
It also means that the mass of cornmeal that is protein is 6% of the total mass of cornmeal or 0.06*x.

 

The total mass of protein from the mixture needs to be 7% or 0.07*240.

 

Therefore, the second equation is:

0.12x+0.06y = 0.07*240, simplified, this is 0.12x+0.06y = 16.8

 

Now we can solve.

 

1) x+y = 240, rearranging so that x is on the left side of the equation, we get x = 240 - y

 

2) 0.12x+0.06y = 16.8, from step 1 we can substitute x into this equation: 0.12*(240-y) + 0.06y = 16.8

 

3) simplifying, this gives 28.8 - 0.12y + 0.06y = 16.8, further simplifying by solving for y , 0.06y = 12, and therefore y = 200lbs. This means that you need 200lbs of cornmeal.

 

4) To solve for how many pounds of soybean meal, substitute y into the equation from step 1: x = 240 - 200 = 40lbs. Therefore, you need 40lbs of soybean meal.

 

That solves the problem! To get 7% protein in a 240lb mixture of soybean meal and cornmeal, you need 40 pounds of soybean meal and 200 pounds of cornmeal.