Dylan had three boxes, containing a total of 660 plastic plates. The number of plastic plates in Box J to the total number of plastic plates was 3 : 11. He sold 354 plastic plates from Box K and sold ¹₃ of the plastic plates in Box L. The number of plastic plates left in Box K to the number of plastic plates left in Box L was 2 : 1. How many plastic plates were there in Box K at first?

	Box J	Box K	Box L	Total
Before	3 u	8 u (480)		11 u (660)
		4 p + 354	3 p
Change		- 354	- 1 p
			2 p
After		2x2 = 4 p	1x2 = 2 p

11 u = 660
1 u = 660 ÷ 11 = 60

Number of plastic plates in Box K and Box L at first
= 8 u
= 8 x 60
= 480

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

4 p + 354 + 3 p = 480
4 p + 3 p = 480 - 354
7 p = 126

1 p = 126 ÷ 7 = 18

Number of plates in Box K at first
= 4 p + 354
= 4 x 18 + 354
= 72 + 354
= 426

Answer(s):426