Luke had three boxes, containing a total of 600 paper bowls. The number of paper bowls in Box V to the total number of paper bowls was 3 : 10. He sold 260 paper bowls from Box W and sold ¹₄ of the paper bowls in Box X. The number of paper bowls left in Box W to the number of paper bowls left in Box X was 4 : 1. How many paper bowls were there in Box W at first?

	Box V	Box W	Box X	Total
Before	3 u	7 u (420)		10 u (600)
		12 p + 260	4 p
Change		- 260	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

10 u = 600
1 u = 600 ÷ 10 = 60

Number of paper bowls in Box W and Box X at first
= 7 u
= 7 x 60
= 420

The number of bowls left in X is the repeated identity.
LCM of 1 and 3 = 3

12 p + 260 + 4 p = 420
12 p + 4 p = 420 - 260
16 p = 160

1 p = 160 ÷ 16 = 10

Number of bowls in Box W at first
= 12 p + 260
= 12 x 10 + 260
= 120 + 260
= 380

Answer(s):380