Cole had three boxes, containing a total of 1400 styrofoam plates. The number of styrofoam plates in Box U to the total number of styrofoam plates was 3 : 10. He sold 455 styrofoam plates from Box V and sold ¹₃ of the styrofoam plates in Box W. The number of styrofoam plates left in Box V to the number of styrofoam plates left in Box W was 2 : 1. How many styrofoam plates were there in Box V at first?

	Box U	Box V	Box W	Total
Before	3 u	7 u (980)		10 u (1400)
		4 p + 455	3 p
Change		- 455	- 1 p
			2 p
After		2x2 = 4 p	1x2 = 2 p

10 u = 1400
1 u = 1400 ÷ 10 = 140

Number of styrofoam plates in Box V and Box W at first
= 7 u
= 7 x 140
= 980

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

4 p + 455 + 3 p = 980
4 p + 3 p = 980 - 455
7 p = 525

1 p = 525 ÷ 7 = 75

Number of plates in Box V at first
= 4 p + 455
= 4 x 75 + 455
= 300 + 455
= 755

Answer(s):755