Soybeal meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240 lb mixture that is 10% protein?

1 Answer
Tony B
Jul 29, 2018

160 pound of Soybeal (did you mean soya bean?)

80 pound Cornmeal

Explanation:

The key point is that you need as many equations as the count of unknown values.

Let the amount of Soybeal meal be #s#
Let the amount of cornmeal be #c#

Then by protein content we have:

#12%s+6%c=10%xx240^("lb")" "......................Equation(1)#

We have two unknowns ans just one equation so we need th build another equation.

We know that the total blend weighs #240^("lb")# so we can use this.

#s+c=240^("lb") color(white)("ddd")=> color(white)("ddd")s=240^("lb") -c" ".......Equation(2)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using #Eqn(2)# substitute for #s# in #Eqn(1)# giving:

#12%(240^("lb")-c)+6%c=10%xx240^("lb")" "......Equation(1_a)#

Dropping the units of measurement for now we have:

#12/100(240-c)+6/100c=10/100xx240#

#28.8-0.12c+0.06c=24#

#-0.06c =-4.8#

#c=(-4.8)/(-0.06)=+80#

This #s=240-80 = 160#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check

Objective is: Left hand side = Right hand side

#(12%xx160)+ (6%xx80) -> 10%xx240#

#19.2+4.8=24#

#24=24 larr" True thus correct"#

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