SOLUTION: Please help me solve: Soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280lbs mixture that is 12% protein?

Question 198842: Please help me solve:
Soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280lbs mixture that is 12% protein?
How many pounds of the cornmeal should be in the misture?
How many pounds of the soybean should be in the mixture?
Thank you.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
let x= # of pounds of soybean meal and y=# of pounds of cornmeal

Since we want a 280 lbs mixture, this means that we have the first equation:

Also, because we want a "280-lb mixture that is 12% protein" from the mixture of
soybean meal that is 14% protein and cornmeal that is 7% protein, we have the second equation:

Start with the second equation.

Multiply

Multiply both sides by 100 to remove the decimals

Distribute

So we have the new system of equations:

Let's solve the system by use of substitution

Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.

So let's isolate y in the first equation

Start with the first equation

Subtract from both sides

Rearrange the equation

---------------------

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute to

Multiply

Combine like terms on the left side

Subtract 1960 from both sides

Combine like terms on the right side

Divide both sides by 7 to isolate x

Divide

-----------------First Answer------------------------------

So the first part of our answer is:

Since we know that we can plug it into the equation (remember we previously solved for in the first equation).

Start with the equation where was previously isolated.

Plug in

Multiply

Combine like terms

-----------------Second Answer------------------------------

So the second part of our answer is:

-----------------Summary------------------------------

So our answers are:

and which form the ordered pair (200,80)

So 200 pounds of soybean meal and 80 pounds of cornmeal are needed for the mixture.

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