Archie had three boxes, containing a total of 560 styrofoam plates. The number of styrofoam plates in Box U to the total number of styrofoam plates was 3 : 8. He sold 260 styrofoam plates from Box V and sold ¹₄ 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	5 u (350)		8 u (560)
		6 p + 260	4 p
Change		- 260	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

8 u = 560
1 u = 560 ÷ 8 = 70

Number of styrofoam plates in Box V and Box W at first
= 5 u
= 5 x 70
= 350

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

6 p + 260 + 4 p = 350
6 p + 4 p = 350 - 260
10 p = 90

1 p = 90 ÷ 10 = 9

Number of plates in Box V at first
= 6 p + 260
= 6 x 9 + 260
= 54 + 260
= 314

Answer(s):314