SOLUTION: Soybean meal is 16% protein, cornmeal is 8%. How many ponds of each would I need to make 380 lbs at 15% protein?

Question 189622: Soybean meal is 16% protein, cornmeal is 8%. How many ponds of each would I need to make 380 lbs at 15% protein?
Answer by greta_elisif(10) (Show Source): You can put this solution on YOUR website!
1. Define your variables:
s = soybean meal used, in pounds
c = cornmeal used, in pounds
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2. Set up the first equation to be solved:

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3. Solve for one variable by subtracting the other from both sides:

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3. Define the amount of protein in each component and in the mixture:
.08c = protein in the cornmeal, in pounds
.16s = protein in the soybean meal, in pounds
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4. With substitution of your answer for s,
= protein in the soybean meal, in pounds
= protein in the mixture, in pounds
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5. Since the amount of protein in the mixture equals the sum of the amounts of protein in the components, the following equation can be made:

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6. Solve the equation for c; distribute .16:

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7. …simplify the variable terms:

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8. …simplify the right side of the equation:

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9. …subtract 60.8 from both sides:

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10. …and divide both sides by -.08:

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11. Having c, use to find s, by replacing the variable and subtracting:

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12. Combine the answers with the variable definitions to write the answer:
I would need 332.5 lbs of soybean meal and 47.5 lbs of cornmeal to make 380 lbs at 15% protein.
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13. To check, replace variables with their equivalents in each equation and solve each one:

Add the two numbers on the left to get:

and

Subtract 47.5 from 380 to get:

Multiply .16 by 332.5 to get:

Multiply .08 by 47.5 to get:

Add 3.8 to 53.2 to get:

Multiply .15 by 380 to get:

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