Jack had three boxes, containing a total of 800 plastic bowls. The number of plastic bowls in Box L to the total number of plastic bowls was 3 : 10. He sold 497 plastic bowls from Box M and sold ¹₃ of the plastic bowls in Box N. The number of plastic bowls left in Box M to the number of plastic bowls left in Box N was 3 : 1. How many plastic bowls 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 + 497	3 p
Change		- 497	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

10 u = 800
1 u = 800 ÷ 10 = 80

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

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

6 p + 497 + 3 p = 560
6 p + 3 p = 560 - 497
9 p = 63

1 p = 63 ÷ 9 = 7

Number of bowls in Box M at first
= 6 p + 497
= 6 x 7 + 497
= 42 + 497
= 539

Answer(s):539