David had three boxes, containing a total of 1100 styrofoam plates. The number of styrofoam plates in Box W to the total number of styrofoam plates was 3 : 11. He sold 320 styrofoam plates from Box X and sold ¹₄ of the styrofoam plates in Box Y. The number of styrofoam plates left in Box X to the number of styrofoam plates left in Box Y was 4 : 1. How many styrofoam plates were there in Box X at first?

	Box W	Box X	Box Y	Total
Before	3 u	8 u (800)		11 u (1100)
		12 p + 320	4 p
Change		- 320	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

11 u = 1100
1 u = 1100 ÷ 11 = 100

Number of styrofoam plates in Box X and Box Y at first
= 8 u
= 8 x 100
= 800

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

12 p + 320 + 4 p = 800
12 p + 4 p = 800 - 320
16 p = 480

1 p = 480 ÷ 16 = 30

Number of plates in Box X at first
= 12 p + 320
= 12 x 30 + 320
= 360 + 320
= 680

Answer(s):680