Question

A cup 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?

Answer 1

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.