Zane had three boxes, containing a total of 800 plastic plates. The number of plastic plates in Box L to the total number of plastic plates was 3 : 10. He sold 385 plastic plates from Box M and sold ¹₃ of the plastic plates in Box N. The number of plastic plates left in Box M to the number of plastic plates left in Box N was 2 : 1. How many plastic plates were there in Box M at first?

	Box L	Box M	Box N	Total
Before	3 u	7 u (560)		10 u (800)
		4 p + 385	3 p
Change		- 385	- 1 p
			2 p
After		2x2 = 4 p	1x2 = 2 p

10 u = 800
1 u = 800 ÷ 10 = 80

Number of plastic plates in Box M and Box N at first
= 7 u
= 7 x 80
= 560

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

4 p + 385 + 3 p = 560
4 p + 3 p = 560 - 385
7 p = 175

1 p = 175 ÷ 7 = 25

Number of plates in Box M at first
= 4 p + 385
= 4 x 25 + 385
= 100 + 385
= 485

Answer(s):485