Seth had three boxes, containing a total of 1300 styrofoam cups. The number of styrofoam cups in Box L to the total number of styrofoam cups was 3 : 10. He sold 280 styrofoam cups from Box M and sold ¹₃ of the styrofoam cups in Box N. The number of styrofoam cups left in Box M to the number of styrofoam cups left in Box N was 2 : 1. How many styrofoam cups were there in Box M at first?

	Box L	Box M	Box N	Total
Before	3 u	7 u (910)		10 u (1300)
		4 p + 280	3 p
Change		- 280	- 1 p
			2 p
After		2x2 = 4 p	1x2 = 2 p

10 u = 1300
1 u = 1300 ÷ 10 = 130

Number of styrofoam cups in Box M and Box N at first
= 7 u
= 7 x 130
= 910

The number of cups left in N is the repeated identity.
LCM of 1 and 2 = 2

4 p + 280 + 3 p = 910
4 p + 3 p = 910 - 280
7 p = 630

1 p = 630 ÷ 7 = 90

Number of cups in Box M at first
= 4 p + 280
= 4 x 90 + 280
= 360 + 280
= 640

Answer(s):640