Valen had three boxes, containing a total of 900 paper plates. The number of paper plates in Box L to the total number of paper plates was 3 : 10. He sold 292 paper plates from Box M and sold ¹₅ of the paper plates in Box N. The number of paper plates left in Box M to the number of paper plates left in Box N was 2 : 1. How many paper plates were there in Box M at first?

	Box L	Box M	Box N	Total
Before	3 u	7 u (630)		10 u (900)
		8 p + 292	5 p
Change		- 292	- 1 p
			4 p
After		2x4 = 8 p	1x4 = 4 p

10 u = 900
1 u = 900 ÷ 10 = 90

Number of paper plates in Box M and Box N at first
= 7 u
= 7 x 90
= 630

The number of plates left in N is the repeated identity.
LCM of 1 and 4 = 4

8 p + 292 + 5 p = 630
8 p + 5 p = 630 - 292
13 p = 338

1 p = 338 ÷ 13 = 26

Number of plates in Box M at first
= 8 p + 292
= 8 x 26 + 292
= 208 + 292
= 500

Answer(s):500