Oliver had three boxes, containing a total of 440 styrofoam plates. The number of styrofoam plates in Box W to the total number of styrofoam plates was 3 : 11. He sold 260 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 2 : 1. How many styrofoam plates were there in Box X at first?

	Box W	Box X	Box Y	Total
Before	3 u	8 u (320)		11 u (440)
		6 p + 260	4 p
Change		- 260	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

11 u = 440
1 u = 440 ÷ 11 = 40

Number of styrofoam plates in Box X and Box Y at first
= 8 u
= 8 x 40
= 320

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

6 p + 260 + 4 p = 320
6 p + 4 p = 320 - 260
10 p = 60

1 p = 60 ÷ 10 = 6

Number of plates in Box X at first
= 6 p + 260
= 6 x 6 + 260
= 36 + 260
= 296

Answer(s):296