Ernie went to the store and bought 33 apples. He bought three times as many red apples as he bought green, and he bought one-half as many yellow as he did red. How many of each type of apple did he buy?

(r is red, g is green and y is yellow)

r+g+y=33

r=3g

2y=r

substitution:

y=33-g-r

y=33 - (1/3) 2y+2y

y=33-8/3y

11/3y=33

y=33: (11/3)

y=9

Solve for red and green:

r=2y

r=2*9

r=18

3g=r

3g=18

g=18/3

g=6

double check:

6+18+9=33

answer:

6 green apples, 9 yellow apples and 18 red apples.