Wesley had three boxes, containing a total of 960 plastic plates. The number of plastic plates in Box N to the total number of plastic plates was 3 : 8. He sold 467 plastic plates from Box P and sold ¹₃ 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	5 u (600)		8 u (960)
		4 p + 467	3 p
Change		- 467	- 1 p
			2 p
After		2x2 = 4 p	1x2 = 2 p

8 u = 960
1 u = 960 ÷ 8 = 120

Number of plastic plates in Box P and Box Q at first
= 5 u
= 5 x 120
= 600

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

4 p + 467 + 3 p = 600
4 p + 3 p = 600 - 467
7 p = 133

1 p = 133 ÷ 7 = 19

Number of plates in Box P at first
= 4 p + 467
= 4 x 19 + 467
= 76 + 467
= 543

Answer(s):543