Luis had three boxes, containing a total of 1100 paper plates. The number of paper plates in Box J to the total number of paper plates was 3 : 11. He sold 477 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 5 : 1. How many paper plates were there in Box K at first?

	Box J	Box K	Box L	Total
Before	3 u	8 u (800)		11 u (1100)
		15 p + 477	4 p
Change		- 477	- 1 p
			3 p
After		5x3 = 15 p	1x3 = 3 p

11 u = 1100
1 u = 1100 ÷ 11 = 100

Number of paper plates in Box K and Box L at first
= 8 u
= 8 x 100
= 800

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

15 p + 477 + 4 p = 800
15 p + 4 p = 800 - 477
19 p = 323

1 p = 323 ÷ 19 = 17

Number of plates in Box K at first
= 15 p + 477
= 15 x 17 + 477
= 255 + 477
= 732

Answer(s):732