Ken had three boxes, containing a total of 770 paper bowls. The number of paper bowls in Box V to the total number of paper bowls was 3 : 7. He sold 352 paper bowls from Box W and sold ¹₃ 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	4 u (440)		7 u (770)
		8 p + 352	3 p
Change		- 352	- 1 p
			2 p
After		4x2 = 8 p	1x2 = 2 p

7 u = 770
1 u = 770 ÷ 7 = 110

Number of paper bowls in Box W and Box X at first
= 4 u
= 4 x 110
= 440

The number of bowls left in X is the repeated identity.
LCM of 1 and 2 = 2

8 p + 352 + 3 p = 440
8 p + 3 p = 440 - 352
11 p = 88

1 p = 88 ÷ 11 = 8

Number of bowls in Box W at first
= 8 p + 352
= 8 x 8 + 352
= 64 + 352
= 416

Answer(s):416