Question

soybean meal is 18% protein cornmeal is 9% protein how many pound of each should be mixed together in order to get 360lb mixture that is 16% protein

Answer 1

god i love this problem.
put x = number of pounds of soybean. since the total is 360 then the amount of cornmeal must be
\[360-x\] since they have to total 360

Answer 2

you get 18% protein from soybean, so it contributes
\[.18x\] and likewise the cornmeal contributes
\[.09(360-x)\]

Answer 3

when you combine them you have to get 16% of 360 =
\[.16\times 360=57.6\] so set
\[.18x+.09(360-x)=57.6\] and solve for x

Answer 4

so it would be x=57.6

Answer 5

oh no, we still have to solve
\[.18x+.09(360-x)=57.6\] for x

Answer 6

i would multiply everything by 100 to get rid of the annoying decimals and write
\[18x+9(360-x)=5760\]

Answer 7

then
\[18x+3240-9x=5760\]
\[9x+3240=5760\]
\[9x=2520\] and finally
\[x=\frac{5250}{9}=580\]

Answer 8

hold the phone i made a mistake let me find it

Answer 9

oh right
last line should be
\[x=\frac{2520}{9}=280\]

Answer 10

so 280 pounds of soy, the rest cornmeal

Answer 11

cornmeal would be the same