Eric had three boxes, containing a total of 1500 styrofoam cups. The number of styrofoam cups in Box X to the total number of styrofoam cups was 3 : 10. He sold 423 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 5 : 1. How many styrofoam cups were there in Box Y at first?

	Box X	Box Y	Box Z	Total
Before	3 u	7 u (1050)		10 u (1500)
		15 p + 423	4 p
Change		- 423	- 1 p
			3 p
After		5x3 = 15 p	1x3 = 3 p

10 u = 1500
1 u = 1500 ÷ 10 = 150

Number of styrofoam cups in Box Y and Box Z at first
= 7 u
= 7 x 150
= 1050

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

15 p + 423 + 4 p = 1050
15 p + 4 p = 1050 - 423
19 p = 627

1 p = 627 ÷ 19 = 33

Number of cups in Box Y at first
= 15 p + 423
= 15 x 33 + 423
= 495 + 423
= 918

Answer(s):918