Dylan had three boxes, containing a total of 880 paper cups. The number of paper cups in Box W to the total number of paper cups was 3 : 11. He sold 368 paper cups from Box X and sold ¹₅ of the paper cups in Box Y. The number of paper cups left in Box X to the number of paper cups left in Box Y was 3 : 1. How many paper cups were there in Box X at first?

	Box W	Box X	Box Y	Total
Before	3 u	8 u (640)		11 u (880)
		12 p + 368	5 p
Change		- 368	- 1 p
			4 p
After		3x4 = 12 p	1x4 = 4 p

11 u = 880
1 u = 880 ÷ 11 = 80

Number of paper cups in Box X and Box Y at first
= 8 u
= 8 x 80
= 640

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

12 p + 368 + 5 p = 640
12 p + 5 p = 640 - 368
17 p = 272

1 p = 272 ÷ 17 = 16

Number of cups in Box X at first
= 12 p + 368
= 12 x 16 + 368
= 192 + 368
= 560

Answer(s):560