soybean 16% protein corn is 9% proteinHow many pounds of each should be mixed to get a 350lb mixture thats 12% protein

Question

solving word problems using linear equations. can you put the equation so I can use the subsitution method or elimination method? thanks

Answer 1

Let amount of soybean be S lb, corn C lb. S+C=350. The amount of protein is 16S/100+9C/100. This must be 12% of the mixture, (16S+9C)/(100*350)=12/100, so (16S+9C)/350=12 or 16S+9C=4200=16S+9(350-S)=7S+3150, from which S=(4200-3150)/7=150, making C=200. So the amount of soybean is 150lb and the amount of corn is 200lb.

CHECK:

150lb soybean yields 24lb of protein, 200lb corn yields 18lb of protein. Total protein: 42lb.

%ge protein: 42/350=0.12=12%