Rael had three boxes, containing a total of 900 styrofoam cups. The number of styrofoam cups in Box M to the total number of styrofoam cups was 3 : 10. He sold 490 styrofoam cups from Box N and sold ¹₄ of the styrofoam cups in Box P. The number of styrofoam cups left in Box N to the number of styrofoam cups left in Box P was 2 : 1. How many styrofoam cups were there in Box N at first?

	Box M	Box N	Box P	Total
Before	3 u	7 u (630)		10 u (900)
		6 p + 490	4 p
Change		- 490	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

10 u = 900
1 u = 900 ÷ 10 = 90

Number of styrofoam cups in Box N and Box P at first
= 7 u
= 7 x 90
= 630

The number of cups left in P is the repeated identity.
LCM of 1 and 3 = 3

6 p + 490 + 4 p = 630
6 p + 4 p = 630 - 490
10 p = 140

1 p = 140 ÷ 10 = 14

Number of cups in Box N at first
= 6 p + 490
= 6 x 14 + 490
= 84 + 490
= 574

Answer(s):574