John had three boxes, containing a total of 880 plastic plates. The number of plastic plates in Box G to the total number of plastic plates was 3 : 11. He sold 332 plastic plates from Box H and sold ¹₃ of the plastic plates in Box J. The number of plastic plates left in Box H to the number of plastic plates left in Box J was 4 : 1. How many plastic plates were there in Box H at first?

	Box G	Box H	Box J	Total
Before	3 u	8 u (640)		11 u (880)
		8 p + 332	3 p
Change		- 332	- 1 p
			2 p
After		4x2 = 8 p	1x2 = 2 p

11 u = 880
1 u = 880 ÷ 11 = 80

Number of plastic plates in Box H and Box J at first
= 8 u
= 8 x 80
= 640

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

8 p + 332 + 3 p = 640
8 p + 3 p = 640 - 332
11 p = 308

1 p = 308 ÷ 11 = 28

Number of plates in Box H at first
= 8 p + 332
= 8 x 28 + 332
= 224 + 332
= 556

Answer(s):556