Elijah had three boxes, containing a total of 1200 styrofoam cups. The number of styrofoam cups in Box F to the total number of styrofoam cups was 3 : 8. He sold 270 styrofoam cups from Box G and sold ¹₄ of the styrofoam cups in Box H. The number of styrofoam cups left in Box G to the number of styrofoam cups left in Box H was 2 : 1. How many styrofoam cups were there in Box G at first?

	Box F	Box G	Box H	Total
Before	3 u	5 u (750)		8 u (1200)
		6 p + 270	4 p
Change		- 270	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

8 u = 1200
1 u = 1200 ÷ 8 = 150

Number of styrofoam cups in Box G and Box H at first
= 5 u
= 5 x 150
= 750

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

6 p + 270 + 4 p = 750
6 p + 4 p = 750 - 270
10 p = 480

1 p = 480 ÷ 10 = 48

Number of cups in Box G at first
= 6 p + 270
= 6 x 48 + 270
= 288 + 270
= 558

Answer(s):558