Question

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?

Answer 1

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"`