Reggie had three boxes, containing a total of 1500 styrofoam bowls. The number of styrofoam bowls in Box M to the total number of styrofoam bowls was 3 : 10. He sold 348 styrofoam bowls from Box N and sold ¹₃ of the styrofoam bowls in Box P. The number of styrofoam bowls left in Box N to the number of styrofoam bowls left in Box P was 3 : 1. How many styrofoam bowls were there in Box N at first?

	Box M	Box N	Box P	Total
Before	3 u	7 u (1050)		10 u (1500)
		6 p + 348	3 p
Change		- 348	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

10 u = 1500
1 u = 1500 ÷ 10 = 150

Number of styrofoam bowls in Box N and Box P at first
= 7 u
= 7 x 150
= 1050

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

6 p + 348 + 3 p = 1050
6 p + 3 p = 1050 - 348
9 p = 702

1 p = 702 ÷ 9 = 78

Number of bowls in Box N at first
= 6 p + 348
= 6 x 78 + 348
= 468 + 348
= 816

Answer(s):816