How many pounds each of a soybean meal at 16 percent protein and cornmeal at 8 percent protein should be mixed together in order to get 320-lb mixture that is 14 percent protein?

Answer 1

Let S be the amount in pounds of soyabean meal and C be the amount in pounds of cornmeal.

You can create two equations relating S & C by considering the amount of protein and total weight:

1. 16% S + 8% C = 14% of 320 lb
2. S + C = 320 lb

which can be used together to solve for S and C:

subtract 6¼ times {1} from {2} to get:

S - 16%S × 6¼ + C - 8% C × 6¼ = 320 - 14 × 6¼ of 320

→ 100% S - 100% S + 100% C - 50% C = 100% of 320 - 87½% of 320

→ 50% C = 12½% of 320

→ C = 25% of 320 = 80

Now substitute for C in {2}:

S + 80 = 320

→ S = 240

Therefore you need 240lb of soyabean meal and 80 lb of cornmeal.

Answer 2

240 lbs of soybean and 80 of cornmeal.