SOLUTION: Soybean meal is 18 percent protein, cornmeal is 9 percent protein. how many pounds of each should be mixed together in order to get 360 pound mixture that is 14 percent protein? H

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Question 271864: Soybean meal is 18 percent protein, cornmeal is 9 percent protein. how many pounds of each should be mixed together in order to get 360 pound mixture that is 14 percent protein?
How many pounds of the cornmeal should be in the mixture?
How many pounds of the soybean meal should be in the mixture?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Soybean is 18% protein.
Cornmeal is 9% protein.
Mixture is 360 pounds and is 14% protein.

let x = amount of soybean.
let y = amount of cornmeal.

One equation is for the amount of soybean and cornmeal in the mixture as shown below:

x + y = 360

The other equation is for the amount of protein in the mixture as shown below:
.18x + .09y = .14 * 360

You need to solve these two equations simultaneously in order to get your answer.

The equations are:

x + y = 360
.18x + .09y = .14*360

Simplify these equations to getr:

x + y = 360
.18x + .09y = 50.4

solve for y in the first equation to get:

y = 360 - x

substitute for y in the second equation to get:

.18x + .09*(360-x) = 50.4

simplify to get:

.18x + .09*360 - .09*x = 50.4

simplify to get:

.18x + 32.4 - .09x = 50.4

combine like terms to get:

.09x + 32.4 = 50.4

subtract 32.4 from both sides of the equation to get:

.09x = 50.4 - 32.4 = 18

divide both sides of this equation by .09 to get:

x = 200

since x + y = 360, this means that y = 160

you have x = 200 and y = 160

substitute in your original equations to see that they are true.

x + y = 360 becomes 200 + 160 = 360 which is true.
.18x + .09y = .14 * 360 becomes .18*200 + .09*160 = .14*360 becomes 36 + 14.4 = 50.4 becomes 50.4 = 50.4 which is true.

since both original equations are true, then the value for x and y are good.

your answer is:

you need 200 pounds of soybeans and 160 pounds of cornmeal.