Question

soybean meal is 14% protein cornmeal is 7% protein. How many counds of each should be mixed together in order to get 280lbs mixture that is 9% protein?

How many pounds of cornmeal
How many pounds of soybean

Answer 1

Put the problem down as an equation
You need to have 280lbs of mixture at 9/100 protein = 280(0.09)
This needs to made up of some mass of soy bean m_S times its percentage of protein plus some mass of cornmeal m_p times its percentage of protein. Thus:
\[280(0.09) = m_s (0.14)+ m_c(0.07)\]

Now, the sum of the masses of soybean and cornmeal must be 280lbs
Therefore
\[280 = m_s +m_c\]
Rearrange this to get it in terms of m_s or m_c, then substitute it into the first equation, so, rearranging to get the mass of soybean:
\[280(0.09) = m_s (0.14) + (280 - m_s)(0.07)\]
Then rearrange to find the mass of soybean:
\[m_s = \left[ 280(0.09)-280(0.07) \right]/(0.14-0.07)\]
The mass of soybean should be 5.6/0.07 = 80lb

Then rearrange the 2nd equation to find the mass of cornmeal. Alternatively just take 80 away from 280 = 200lb. But do the other method just to check :)