Nick had three boxes, containing a total of 960 styrofoam cups. The number of styrofoam cups in Box H to the total number of styrofoam cups was 3 : 8. He sold 366 styrofoam cups from Box J and sold ¹₅ of the styrofoam cups in Box K. The number of styrofoam cups left in Box J to the number of styrofoam cups left in Box K was 2 : 1. How many styrofoam cups were there in Box J at first?

	Box H	Box J	Box K	Total
Before	3 u	5 u (600)		8 u (960)
		8 p + 366	5 p
Change		- 366	- 1 p
			4 p
After		2x4 = 8 p	1x4 = 4 p

8 u = 960
1 u = 960 ÷ 8 = 120

Number of styrofoam cups in Box J and Box K at first
= 5 u
= 5 x 120
= 600

The number of cups left in K is the repeated identity.
LCM of 1 and 4 = 4

8 p + 366 + 5 p = 600
8 p + 5 p = 600 - 366
13 p = 234

1 p = 234 ÷ 13 = 18

Number of cups in Box J at first
= 8 p + 366
= 8 x 18 + 366
= 144 + 366
= 510

Answer(s):510