SOLUTION: Soybean meal is 16% protein; cornmela is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 14% protein? How many pounds of the

Algebra ->  Equations -> SOLUTION: Soybean meal is 16% protein; cornmela is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 14% protein? How many pounds of the       Log On


   

Question 146587: Soybean meal is 16% protein; cornmela is 8% protein. How many pounds of each should be mixed together in order to get 320-lb mixture that is 14% protein?
How many pounds of the cornmeal should be in the mixture?
How many pounds of the soybean should be in the mixture?
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 320 mixture, this means that we have the first equation:
x%2By=320


Also, because we want a "320-lb mixture that is 14% protein" from the mixture of
soybean meal that is 16% protein and "cornmeal that is 8% protein, we have the second equation:

0.16x%2B0.08y=320%280.14%29


0.16x%2B0.08y=44.8 Multiply


10%280.16x%2B0.08y%29=10%2844.8%29 Multiply both sides by 10 to remove the decimals


16x%2B8y=4480 Distribute


So we have the new system of equations:
system%28x%2By=320%2C16x%2B8y=4480%29




x%2By=320 Start with the first equation


y=320-x Subtract x from both sides


y=-x%2B320 Rearrange the equation



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

Since y=-x%2B320, we can now replace each y in the second equation with -x%2B320 to solve for x



16x%2B8highlight%28%28-x%2B320%29%29=4480 Plug in y=-x%2B320 into the first equation. In other words, replace each y with -x%2B320. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



16x%2B%288%29%28-1%29x%2B%288%29%28320%29=4480 Distribute 8 to -x%2B320


16x-8x%2B2560=4480 Multiply


8x%2B2560=4480 Combine like terms on the left side


8x=4480-2560Subtract 2560 from both sides


8x=1920 Combine like terms on the right side


x=%281920%29%2F%288%29 Divide both sides by 8 to isolate x



x=240 Divide





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


So the first part of our answer is: x=240









Since we know that x=240 we can plug it into the equation y=-x%2B320 (remember we previously solved for y in the first equation).



y=-x%2B320 Start with the equation where y was previously isolated.


y=-%28240%29%2B320 Plug in x=240


y=-240%2B320 Multiply


y=80 Combine like terms



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


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









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

So our answers are:

x=240 and y=80

which form the ordered pair



So there are 240 pounds of Soybean meal and 80 pounds of cornmeal