Mrs. Lewis needs to buy two types of grain, oats, and barley to mix as a feed supplement for her cattle. She has $4275 to spend on grain and wants the mixture to be 3 parts oats and 2 parts barley. She can buy oats for $1.10 per bushel and barley for $2.10 per bushel. Mrs. Lewis needs 7,000 bushels of grain. How many bushels of barley should she buy?
Mrs. Lewis cannot buy 7,000 bushels of grain, for that would cost her at least 7,000*$1.10=$7,700, but she only has $4275.
Let X=bushels of oat and Y=bushels of barley. 3 parts oats and 2 parts barley means 2X=3Y, or X=1.5Y. Her cost is 4275=1.1X+2.1Y. Now substitute X=1.5Y and simplify: 4275=1.1(1.5Y)+2.1Y=3.75Y. Therefore, Y=4275/3.75=1140, so she should buy 1140 bushels of barley.