Question

Soybean meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together to get 240-lb mixture that is 11% protein?

Answer 1

To get a 240-lb mixture that is 11% protein, you should mix 200 pounds of soybean meal and 40 pounds of cornmeal.

Step-by-step explanation:

To solve this problem, you can use a system of equations. Let's say you want to mix x pounds of soybean meal and y pounds of cornmeal. Since the total mixture is 240 pounds, we can write the equation x + y = 240. Now let's set up an equation for the protein content. Since soybean meal is 12% protein and cornmeal is 6% protein, the equation becomes 0.12x + 0.06y = 0.11(240).

Now you have a system of equations. You can use the substitution or elimination method to solve for x and y. Let's use the substitution method:

1. Isolate x in the first equation: x = 240 - y
2. Substitute x into the second equation: 0.12(240 - y) + 0.06y = 0.11(240)
3. Solve for y: 28.8 - 0.12y + 0.06y = 26.4
4. Combine like terms: -0.06y = -2.4
5. Divide both sides by -0.06: y = 40
6. Substitute y back into the first equation: x + 40 = 240
7. Solve for x: x = 200

To obtain a 240-pound mixture that is 11% protein, you should mix 200 pounds of soybean meal and 40 pounds of cornmeal.

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