Ryan had three boxes, containing a total of 1000 plastic plates. The number of plastic plates in Box D to the total number of plastic plates was 3 : 10. He sold 462 plastic plates from Box E and sold ¹₅ of the plastic plates in Box F. The number of plastic plates left in Box E to the number of plastic plates left in Box F was 3 : 1. How many plastic plates were there in Box E at first?

	Box D	Box E	Box F	Total
Before	3 u	7 u (700)		10 u (1000)
		12 p + 462	5 p
Change		- 462	- 1 p
			4 p
After		3x4 = 12 p	1x4 = 4 p

10 u = 1000
1 u = 1000 ÷ 10 = 100

Number of plastic plates in Box E and Box F at first
= 7 u
= 7 x 100
= 700

The number of plates left in F is the repeated identity.
LCM of 1 and 4 = 4

12 p + 462 + 5 p = 700
12 p + 5 p = 700 - 462
17 p = 238

1 p = 238 ÷ 17 = 14

Number of plates in Box E at first
= 12 p + 462
= 12 x 14 + 462
= 168 + 462
= 630

Answer(s):630