Flynn had three boxes, containing a total of 1210 styrofoam cups. The number of styrofoam cups in Box X to the total number of styrofoam cups was 3 : 11. He sold 250 styrofoam cups from Box Y and sold ¹₄ of the styrofoam cups in Box Z. The number of styrofoam cups left in Box Y to the number of styrofoam cups left in Box Z was 2 : 1. How many styrofoam cups were there in Box Y at first?

	Box X	Box Y	Box Z	Total
Before	3 u	8 u (880)		11 u (1210)
		6 p + 250	4 p
Change		- 250	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

11 u = 1210
1 u = 1210 ÷ 11 = 110

Number of styrofoam cups in Box Y and Box Z at first
= 8 u
= 8 x 110
= 880

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

6 p + 250 + 4 p = 880
6 p + 4 p = 880 - 250
10 p = 630

1 p = 630 ÷ 10 = 63

Number of cups in Box Y at first
= 6 p + 250
= 6 x 63 + 250
= 378 + 250
= 628

Answer(s):628