Ryan had three boxes, containing a total of 700 paper plates. The number of paper plates in Box F to the total number of paper plates was 3 : 10. He sold 400 paper plates from Box G and sold ¹₃ of the paper plates in Box H. The number of paper plates left in Box G to the number of paper plates left in Box H was 3 : 1. How many paper plates were there in Box G at first?

	Box F	Box G	Box H	Total
Before	3 u	7 u (490)		10 u (700)
		6 p + 400	3 p
Change		- 400	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

10 u = 700
1 u = 700 ÷ 10 = 70

Number of paper plates in Box G and Box H at first
= 7 u
= 7 x 70
= 490

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

6 p + 400 + 3 p = 490
6 p + 3 p = 490 - 400
9 p = 90

1 p = 90 ÷ 9 = 10

Number of plates in Box G at first
= 6 p + 400
= 6 x 10 + 400
= 60 + 400
= 460

Answer(s):460