Gabriel had three boxes, containing a total of 990 paper plates. The number of paper plates in Box J to the total number of paper plates was 3 : 11. He sold 370 paper plates from Box K and sold ¹₄ of the paper plates in Box L. The number of paper plates left in Box K to the number of paper plates left in Box L was 2 : 1. How many paper plates were there in Box K at first?

	Box J	Box K	Box L	Total
Before	3 u	8 u (720)		11 u (990)
		6 p + 370	4 p
Change		- 370	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

11 u = 990
1 u = 990 ÷ 11 = 90

Number of paper plates in Box K and Box L at first
= 8 u
= 8 x 90
= 720

The number of plates left in L is the repeated identity.
LCM of 1 and 3 = 3

6 p + 370 + 4 p = 720
6 p + 4 p = 720 - 370
10 p = 350

1 p = 350 ÷ 10 = 35

Number of plates in Box K at first
= 6 p + 370
= 6 x 35 + 370
= 210 + 370
= 580

Answer(s):580