Daniel had three boxes, containing a total of 480 paper plates. The number of paper plates in Box V to the total number of paper plates was 3 : 8. He sold 255 paper plates from Box W and sold ¹₃ of the paper plates in Box X. The number of paper plates left in Box W to the number of paper plates left in Box X was 3 : 1. How many paper plates were there in Box W at first?

	Box V	Box W	Box X	Total
Before	3 u	5 u (300)		8 u (480)
		6 p + 255	3 p
Change		- 255	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

8 u = 480
1 u = 480 ÷ 8 = 60

Number of paper plates in Box W and Box X at first
= 5 u
= 5 x 60
= 300

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

6 p + 255 + 3 p = 300
6 p + 3 p = 300 - 255
9 p = 45

1 p = 45 ÷ 9 = 5

Number of plates in Box W at first
= 6 p + 255
= 6 x 5 + 255
= 30 + 255
= 285

Answer(s):285