Let x be the number of pounds of cornmeal and let y be the number of pounds of soybean meal. Since the mixture is 280 lbs, we have x + y = 280. Since cornmeal is 7% protein, the number of pounds of protein in the mixture from cornmeal is 0.07x, and since soybean meal is 14% protein, the number of pounds of protein in the mixture from the soybean meal is 0.14y. Moreover, since the mixture is 8% protein, the number of pounds of total protein in the mixture is 280*0.08 = 22.4. Thus, we have 0.07x + 0.14y = 22.4. The problem boils down to solving the following linear system:
x+y = 280
0.07x + 0.14y = 22.4
Solving the first equation for x gives us x = 280 - y.
Substituting this in the second equation, we have 0.07*(280 - y) + 0.14y = 22.4.
Distributing, we have 0.07*280 - 0.07y + 0.14y = 22.4.
Simplifying and combining like terms, we have 19.6 + 0.07y = 22.4.
Subtracting 19.6 from both sides gives us 0.07y = 2.8.
Finally, dividing both sides by 0.07, we have y = 40, so x = 280 - y = 280 - 40 = 240.
Thus, there should be 240 pounds of cornmeal and 40 pounds of soybean meal in the mixture.
