Luke had three boxes, containing a total of 1040 styrofoam cups. The number of styrofoam cups in Box V to the total number of styrofoam cups was 3 : 8. He sold 378 styrofoam cups from Box W and sold ¹₅ of the styrofoam cups in Box X. The number of styrofoam cups left in Box W to the number of styrofoam cups left in Box X was 3 : 1. How many styrofoam cups were there in Box W at first?

	Box V	Box W	Box X	Total
Before	3 u	5 u (650)		8 u (1040)
		12 p + 378	5 p
Change		- 378	- 1 p
			4 p
After		3x4 = 12 p	1x4 = 4 p

8 u = 1040
1 u = 1040 ÷ 8 = 130

Number of styrofoam cups in Box W and Box X at first
= 5 u
= 5 x 130
= 650

The number of cups left in X is the repeated identity.
LCM of 1 and 4 = 4

12 p + 378 + 5 p = 650
12 p + 5 p = 650 - 378
17 p = 272

1 p = 272 ÷ 17 = 16

Number of cups in Box W at first
= 12 p + 378
= 12 x 16 + 378
= 192 + 378
= 570

Answer(s):570