Seth had three boxes, containing a total of 720 paper bowls. The number of paper bowls in Box M to the total number of paper bowls was 3 : 8. He sold 263 paper bowls from Box N and sold ¹₅ of the paper bowls in Box P. The number of paper bowls left in Box N to the number of paper bowls left in Box P was 3 : 1. How many paper bowls were there in Box N at first?

	Box M	Box N	Box P	Total
Before	3 u	5 u (450)		8 u (720)
		12 p + 263	5 p
Change		- 263	- 1 p
			4 p
After		3x4 = 12 p	1x4 = 4 p

8 u = 720
1 u = 720 ÷ 8 = 90

Number of paper bowls in Box N and Box P at first
= 5 u
= 5 x 90
= 450

The number of bowls left in P is the repeated identity.
LCM of 1 and 4 = 4

12 p + 263 + 5 p = 450
12 p + 5 p = 450 - 263
17 p = 187

1 p = 187 ÷ 17 = 11

Number of bowls in Box N at first
= 12 p + 263
= 12 x 11 + 263
= 132 + 263
= 395

Answer(s):395