Acup of rolled oats ( x x) provided 310 310 calories. a cup of wheat flakes ( y y) provided 290 290 calories. a new breakfast cereal combines wheat and oats to provide 302 302 calories per cup. how much of each grain does 1 1 cup of the cereal contain?

Let z be the percent of the cup that is oats.
   Therefore 310*z + 290 * (1-z) = 302.
   310z-290z+290=302.
 20z=12 z=12/20 = .6.
   Therefore the new cereal is 60% oats and 40% wheat flakes.
A cup of the cereal then contains 3/5 cup of oats, and 2/5 cup of wheat flakes.