Ken had three boxes, containing a total of 1200 paper plates. The number of paper plates in Box K to the total number of paper plates was 3 : 8. He sold 288 paper plates from Box L and sold ¹₃ of the paper plates in Box M. The number of paper plates left in Box L to the number of paper plates left in Box M was 2 : 1. How many paper plates were there in Box L at first?

	Box K	Box L	Box M	Total
Before	3 u	5 u (750)		8 u (1200)
		4 p + 288	3 p
Change		- 288	- 1 p
			2 p
After		2x2 = 4 p	1x2 = 2 p

8 u = 1200
1 u = 1200 ÷ 8 = 150

Number of paper plates in Box L and Box M at first
= 5 u
= 5 x 150
= 750

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

4 p + 288 + 3 p = 750
4 p + 3 p = 750 - 288
7 p = 462

1 p = 462 ÷ 7 = 66

Number of plates in Box L at first
= 4 p + 288
= 4 x 66 + 288
= 264 + 288
= 552

Answer(s):552