# 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?

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 ${240}^{\text{lb}}$ so we can use this.

s+c=240^("lb") color(white)("ddd")=> color(white)("ddd")s=240^("lb") -c" ".......Equation(2)
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Using $E q n \left(2\right)$ substitute for $s$ in $E q n \left(1\right)$ giving:

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

Dropping the units of measurement for now we have:

$\frac{12}{100} \left(240 - c\right) + \frac{6}{100} c = \frac{10}{100} \times 240$

$28.8 - 0.12 c + 0.06 c = 24$

$- 0.06 c = - 4.8$

$c = \frac{- 4.8}{- 0.06} = + 80$

This $s = 240 - 80 = 160$
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Check

Objective is: Left hand side = Right hand side

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

$19.2 + 4.8 = 24$

$24 = 24 \leftarrow \text{ True thus correct}$