Glen had three boxes, containing a total of 1100 styrofoam plates. The number of styrofoam plates in Box P to the total number of styrofoam plates was 3 : 11. He sold 488 styrofoam plates from Box Q and sold ¹₃ 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 5 : 1. How many styrofoam plates were there in Box Q at first?

	Box P	Box Q	Box R	Total
Before	3 u	8 u (800)		11 u (1100)
		10 p + 488	3 p
Change		- 488	- 1 p
			2 p
After		5x2 = 10 p	1x2 = 2 p

11 u = 1100
1 u = 1100 ÷ 11 = 100

Number of styrofoam plates in Box Q and Box R at first
= 8 u
= 8 x 100
= 800

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

10 p + 488 + 3 p = 800
10 p + 3 p = 800 - 488
13 p = 312

1 p = 312 ÷ 13 = 24

Number of plates in Box Q at first
= 10 p + 488
= 10 x 24 + 488
= 240 + 488
= 728

Answer(s):728