Brandon had three boxes, containing a total of 1100 paper cups. The number of paper cups in Box F to the total number of paper cups was 3 : 11. He sold 270 paper cups from Box G and sold ¹₄ of the paper cups in Box H. The number of paper cups left in Box G to the number of paper cups left in Box H was 2 : 1. How many paper cups were there in Box G at first?

	Box F	Box G	Box H	Total
Before	3 u	8 u (800)		11 u (1100)
		6 p + 270	4 p
Change		- 270	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

11 u = 1100
1 u = 1100 ÷ 11 = 100

Number of paper cups in Box G and Box H at first
= 8 u
= 8 x 100
= 800

The number of cups left in H is the repeated identity.
LCM of 1 and 3 = 3

6 p + 270 + 4 p = 800
6 p + 4 p = 800 - 270
10 p = 530

1 p = 530 ÷ 10 = 53

Number of cups in Box G at first
= 6 p + 270
= 6 x 53 + 270
= 318 + 270
= 588

Answer(s):588