Vincent had three boxes, containing a total of 990 plastic cups. The number of plastic cups in Box W to the total number of plastic cups was 3 : 11. He sold 464 plastic cups from Box X and sold ¹₄ of the plastic cups in Box Y. The number of plastic cups left in Box X to the number of plastic cups left in Box Y was 4 : 1. How many plastic cups were there in Box X at first?

	Box W	Box X	Box Y	Total
Before	3 u	8 u (720)		11 u (990)
		12 p + 464	4 p
Change		- 464	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

11 u = 990
1 u = 990 ÷ 11 = 90

Number of plastic cups in Box X and Box Y at first
= 8 u
= 8 x 90
= 720

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

12 p + 464 + 4 p = 720
12 p + 4 p = 720 - 464
16 p = 256

1 p = 256 ÷ 16 = 16

Number of cups in Box X at first
= 12 p + 464
= 12 x 16 + 464
= 192 + 464
= 656

Answer(s):656