David had three boxes, containing a total of 700 plastic plates. The number of plastic plates in Box N to the total number of plastic plates was 3 : 10. He sold 269 plastic plates from Box P and sold ¹₅ of the plastic plates in Box Q. The number of plastic plates left in Box P to the number of plastic plates left in Box Q was 2 : 1. How many plastic plates were there in Box P at first?

	Box N	Box P	Box Q	Total
Before	3 u	7 u (490)		10 u (700)
		8 p + 269	5 p
Change		- 269	- 1 p
			4 p
After		2x4 = 8 p	1x4 = 4 p

10 u = 700
1 u = 700 ÷ 10 = 70

Number of plastic plates in Box P and Box Q at first
= 7 u
= 7 x 70
= 490

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

8 p + 269 + 5 p = 490
8 p + 5 p = 490 - 269
13 p = 221

1 p = 221 ÷ 13 = 17

Number of plates in Box P at first
= 8 p + 269
= 8 x 17 + 269
= 136 + 269
= 405

Answer(s):405