Bobby had three boxes, containing a total of 1200 plastic plates. The number of plastic plates in Box M to the total number of plastic plates was 3 : 10. He sold 465 plastic plates from Box N and sold ¹₅ of the plastic plates in Box P. The number of plastic plates left in Box N to the number of plastic plates left in Box P was 5 : 1. How many plastic plates were there in Box N at first?

	Box M	Box N	Box P	Total
Before	3 u	7 u (840)		10 u (1200)
		20 p + 465	5 p
Change		- 465	- 1 p
			4 p
After		5x4 = 20 p	1x4 = 4 p

10 u = 1200
1 u = 1200 ÷ 10 = 120

Number of plastic plates in Box N and Box P at first
= 7 u
= 7 x 120
= 840

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

20 p + 465 + 5 p = 840
20 p + 5 p = 840 - 465
25 p = 375

1 p = 375 ÷ 25 = 15

Number of plates in Box N at first
= 20 p + 465
= 20 x 15 + 465
= 300 + 465
= 765

Answer(s):765