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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?
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:16% S + 8% C = 14% of 320 lbS + C = 320 lbwhich 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 = 80Now substitute for C in {2}:S + 80 = 320→ S = 240Therefore you need 240lb of soyabean meal and 80 lb of cornmeal.
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