Jenson had three boxes, containing a total of 1100 plastic cups. The number of plastic cups in Box U to the total number of plastic cups was 3 : 11. He sold 415 plastic cups from Box V and sold ¹₃ of the plastic cups in Box W. The number of plastic cups left in Box V to the number of plastic cups left in Box W was 4 : 1. How many plastic cups were there in Box V at first?

	Box U	Box V	Box W	Total
Before	3 u	8 u (800)		11 u (1100)
		8 p + 415	3 p
Change		- 415	- 1 p
			2 p
After		4x2 = 8 p	1x2 = 2 p

11 u = 1100
1 u = 1100 ÷ 11 = 100

Number of plastic cups in Box V and Box W at first
= 8 u
= 8 x 100
= 800

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

8 p + 415 + 3 p = 800
8 p + 3 p = 800 - 415
11 p = 385

1 p = 385 ÷ 11 = 35

Number of cups in Box V at first
= 8 p + 415
= 8 x 35 + 415
= 280 + 415
= 695

Answer(s):695