Elijah had three boxes, containing a total of 1650 paper cups. The number of paper cups in Box Q to the total number of paper cups was 3 : 11. He sold 264 paper cups from Box R and sold ¹₅ of the paper cups in Box S. The number of paper cups left in Box R to the number of paper cups left in Box S was 2 : 1. How many paper cups were there in Box R at first?

	Box Q	Box R	Box S	Total
Before	3 u	8 u (1200)		11 u (1650)
		8 p + 264	5 p
Change		- 264	- 1 p
			4 p
After		2x4 = 8 p	1x4 = 4 p

11 u = 1650
1 u = 1650 ÷ 11 = 150

Number of paper cups in Box R and Box S at first
= 8 u
= 8 x 150
= 1200

The number of cups left in S is the repeated identity.
LCM of 1 and 4 = 4

8 p + 264 + 5 p = 1200
8 p + 5 p = 1200 - 264
13 p = 936

1 p = 936 ÷ 13 = 72

Number of cups in Box R at first
= 8 p + 264
= 8 x 72 + 264
= 576 + 264
= 840

Answer(s):840