Question

Soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together to get 280 lb mixture that is 13% protien?

Answer 1

you can solve this using a system

Answer 2

start with
\[0.14x+0.7(280-x)=0.13\times 280\]

Answer 3

the maybe multiply by 100 get rid of annoying decimals and get
\[14x+7(280-x)=3640\] good from there?

Answer 4

oh and typo in first line it should be
\[0.14x+0.07(280-x)=0.13\times 280\] reasoning that if you put x = amount of soybean then it contributes 14% of x i.e. .14x to the mixture, and if x = amount of soybean then since the total is 280 the amount of corn must be 280 - x which contributes 7% or .07(280-x) protein.
add these up and set it equal to 13% of 280 = .13 times 280

Answer 5

if i recall my cramer rightly; it might go like this

amount @ 14% = 280(13% - 7%)/(14% - 7%)

Answer 6

and its other part would amount to:

amount @ 7% = 280(13% - 14%)/(7%-14%)

amount @ 7% = 280(-.01)/(-.07)