Liam had three boxes, containing a total of 1650 styrofoam plates. The number of styrofoam plates in Box P to the total number of styrofoam plates was 3 : 11. He sold 380 styrofoam plates from Box Q and sold ¹₄ of the styrofoam plates in Box R. The number of styrofoam plates left in Box Q to the number of styrofoam plates left in Box R was 2 : 1. How many styrofoam plates were there in Box Q at first?

	Box P	Box Q	Box R	Total
Before	3 u	8 u (1200)		11 u (1650)
		6 p + 380	4 p
Change		- 380	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

11 u = 1650
1 u = 1650 ÷ 11 = 150

Number of styrofoam plates in Box Q and Box R at first
= 8 u
= 8 x 150
= 1200

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

6 p + 380 + 4 p = 1200
6 p + 4 p = 1200 - 380
10 p = 820

1 p = 820 ÷ 10 = 82

Number of plates in Box Q at first
= 6 p + 380
= 6 x 82 + 380
= 492 + 380
= 872

Answer(s):872