Lee had three boxes, containing a total of 1430 plastic plates. The number of plastic plates in Box U to the total number of plastic plates was 3 : 11. He sold 319 plastic plates from Box V and sold ¹₃ of the plastic plates in Box W. The number of plastic plates left in Box V to the number of plastic plates left in Box W was 2 : 1. How many plastic plates were there in Box V at first?

	Box U	Box V	Box W	Total
Before	3 u	8 u (1040)		11 u (1430)
		4 p + 319	3 p
Change		- 319	- 1 p
			2 p
After		2x2 = 4 p	1x2 = 2 p

11 u = 1430
1 u = 1430 ÷ 11 = 130

Number of plastic plates in Box V and Box W at first
= 8 u
= 8 x 130
= 1040

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

4 p + 319 + 3 p = 1040
4 p + 3 p = 1040 - 319
7 p = 721

1 p = 721 ÷ 7 = 103

Number of plates in Box V at first
= 4 p + 319
= 4 x 103 + 319
= 412 + 319
= 731

Answer(s):731