Question

There were some green and red apples in a box. Ted took up 2/11 of the green apples from the box. He replaced each of these green apples taken out with red apples. After that, he took out 2/5 of the green apples and 1/3 of the red apples. There were 108 green apples and 228 red apples left in the box in the end. What was the total number of green and red apples in the box at first?

Answer 1

to start, let there be g green and r red apples.
The amounts change after each step
9/11 g and r
9/11g and (r + 2/11 g)
3/5 (9/11 g) = 108
2/3 (r + 2/11 g) = 228
so, we have
g = 220 and r = 302

Answer 2

Here's another approach:
Focus on just green apples first.
g - (2/11)g -(2/5)(9/11)g = 108
Solve to find g = 220
Now red apples.
r + (2/11)(220) - (1/3)(r + (2/11)(220))
Solve to find r = 302