Liam had three boxes, containing a total of 1430 plastic cups. The number of plastic cups in Box V to the total number of plastic cups was 3 : 11. He sold 270 plastic cups from Box W and sold ¹₃ of the plastic cups in Box X. The number of plastic cups left in Box W to the number of plastic cups left in Box X was 4 : 1. How many plastic cups were there in Box W at first?

	Box V	Box W	Box X	Total
Before	3 u	8 u (1040)		11 u (1430)
		8 p + 270	3 p
Change		- 270	- 1 p
			2 p
After		4x2 = 8 p	1x2 = 2 p

11 u = 1430
1 u = 1430 ÷ 11 = 130

Number of plastic cups in Box W and Box X at first
= 8 u
= 8 x 130
= 1040

The number of cups left in X is the repeated identity.
LCM of 1 and 2 = 2

8 p + 270 + 3 p = 1040
8 p + 3 p = 1040 - 270
11 p = 770

1 p = 770 ÷ 11 = 70

Number of cups in Box W at first
= 8 p + 270
= 8 x 70 + 270
= 560 + 270
= 830

Answer(s):830