Cody had three boxes, containing a total of 800 paper plates. The number of paper plates in Box L to the total number of paper plates was 3 : 10. He sold 254 paper plates from Box M and sold ¹₃ 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 3 : 1. How many paper plates were there in Box M at first?

	Box L	Box M	Box N	Total
Before	3 u	7 u (560)		10 u (800)
		6 p + 254	3 p
Change		- 254	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

10 u = 800
1 u = 800 ÷ 10 = 80

Number of paper 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

6 p + 254 + 3 p = 560
6 p + 3 p = 560 - 254
9 p = 306

1 p = 306 ÷ 9 = 34

Number of plates in Box M at first
= 6 p + 254
= 6 x 34 + 254
= 204 + 254
= 458

Answer(s):458