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?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> 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?       Log On


   

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) About Me  (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:
x%2By=280


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: 0.14x%2B0.07y=280%280.12%29



0.14x%2B0.07y=280%280.12%29 Start with the second equation.


0.14x%2B0.07y=33.6 Multiply


10%280.14x%2B0.07y%29=10%2833.6%29 Multiply both sides by 100 to remove the decimals


14x%2B7y=3360 Distribute


So we have the new system of equations:

system%28x%2By=280%2C14x%2B7y=3360%29


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


x%2By=280 Start with the first equation


y=280-x Subtract x from both sides


y=-x%2B280 Rearrange the equation


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

Since y=-x%2B280, we can now replace each y in the second equation with -x%2B280 to solve for x



14x%2B7highlight%28%28-x%2B280%29%29=3360 Plug in y=-x%2B280 into the second equation. In other words, replace each y with -x%2B280. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



14x%2B%287%29%28-1%29x+%2B+%287%29%28280%29=3360 Distribute 7 to -x%2B280


14x-7x%2B1960=3360 Multiply


7x%2B1960=3360 Combine like terms on the left side


7x=3360-1960Subtract 1960 from both sides


7x=1400 Combine like terms on the right side


x=%281400%29%2F%287%29 Divide both sides by 7 to isolate x


x=200 Divide



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


So the first part of our answer is: x=200



Since we know that x=200 we can plug it into the equation y=-x%2B280 (remember we previously solved for y in the first equation).



y=-x%2B280 Start with the equation where y was previously isolated.


y=-%28200%29%2B280 Plug in x=200


y=-200%2B280 Multiply


y=80 Combine like terms



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


So the second part of our answer is: y=80






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

So our answers are:

x=200 and y=80 which form the ordered pair (200,80)



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