Perry had three boxes, containing a total of 800 plastic plates. The number of plastic plates in Box F to the total number of plastic plates was 3 : 10. He sold 273 plastic plates from Box G and sold ¹₃ of the plastic plates in Box H. The number of plastic plates left in Box G to the number of plastic plates left in Box H was 2 : 1. How many plastic plates were there in Box G at first?

	Box F	Box G	Box H	Total
Before	3 u	7 u (560)		10 u (800)
		4 p + 273	3 p
Change		- 273	- 1 p
			2 p
After		2x2 = 4 p	1x2 = 2 p

10 u = 800
1 u = 800 ÷ 10 = 80

Number of plastic plates in Box G and Box H at first
= 7 u
= 7 x 80
= 560

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

4 p + 273 + 3 p = 560
4 p + 3 p = 560 - 273
7 p = 287

1 p = 287 ÷ 7 = 41

Number of plates in Box G at first
= 4 p + 273
= 4 x 41 + 273
= 164 + 273
= 437

Answer(s):437