Ryan had three boxes, containing a total of 700 paper plates. The number of paper plates in Box U to the total number of paper plates was 3 : 10. He sold 415 paper plates from Box V and sold ¹₅ of the paper plates in Box W. The number of paper plates left in Box V to the number of paper plates left in Box W was 5 : 1. How many paper plates were there in Box V at first?

	Box U	Box V	Box W	Total
Before	3 u	7 u (490)		10 u (700)
		20 p + 415	5 p
Change		- 415	- 1 p
			4 p
After		5x4 = 20 p	1x4 = 4 p

10 u = 700
1 u = 700 ÷ 10 = 70

Number of paper plates in Box V and Box W at first
= 7 u
= 7 x 70
= 490

The number of plates left in W is the repeated identity.
LCM of 1 and 4 = 4

20 p + 415 + 5 p = 490
20 p + 5 p = 490 - 415
25 p = 75

1 p = 75 ÷ 25 = 3

Number of plates in Box V at first
= 20 p + 415
= 20 x 3 + 415
= 60 + 415
= 475

Answer(s):475