Luis had three boxes, containing a total of 880 plastic plates. The number of plastic plates in Box P to the total number of plastic plates was 3 : 8. He sold 340 plastic plates from Box Q and sold ¹₄ of the plastic plates in Box R. The number of plastic plates left in Box Q to the number of plastic plates left in Box R was 2 : 1. How many plastic plates were there in Box Q at first?

	Box P	Box Q	Box R	Total
Before	3 u	5 u (550)		8 u (880)
		6 p + 340	4 p
Change		- 340	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

8 u = 880
1 u = 880 ÷ 8 = 110

Number of plastic plates in Box Q and Box R at first
= 5 u
= 5 x 110
= 550

The number of plates left in R is the repeated identity.
LCM of 1 and 3 = 3

6 p + 340 + 4 p = 550
6 p + 4 p = 550 - 340
10 p = 210

1 p = 210 ÷ 10 = 21

Number of plates in Box Q at first
= 6 p + 340
= 6 x 21 + 340
= 126 + 340
= 466

Answer(s):466