Ian had three boxes, containing a total of 980 paper plates. The number of paper plates in Box K to the total number of paper plates was 3 : 7. He sold 496 paper plates from Box L and sold ¹₄ 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 4 : 1. How many paper plates were there in Box L at first?

	Box K	Box L	Box M	Total
Before	3 u	4 u (560)		7 u (980)
		12 p + 496	4 p
Change		- 496	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

7 u = 980
1 u = 980 ÷ 7 = 140

Number of paper plates in Box L and Box M at first
= 4 u
= 4 x 140
= 560

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

12 p + 496 + 4 p = 560
12 p + 4 p = 560 - 496
16 p = 64

1 p = 64 ÷ 16 = 4

Number of plates in Box L at first
= 12 p + 496
= 12 x 4 + 496
= 48 + 496
= 544

Answer(s):544