Jenson had three boxes, containing a total of 1100 styrofoam cups. The number of styrofoam cups in Box H to the total number of styrofoam cups was 3 : 10. He sold 270 styrofoam cups from Box J and sold ¹₄ 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	7 u (770)		10 u (1100)
		6 p + 270	4 p
Change		- 270	- 1 p
			3 p
After		2x3 = 6 p	1x3 = 3 p

10 u = 1100
1 u = 1100 ÷ 10 = 110

Number of styrofoam cups in Box J and Box K at first
= 7 u
= 7 x 110
= 770

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

6 p + 270 + 4 p = 770
6 p + 4 p = 770 - 270
10 p = 500

1 p = 500 ÷ 10 = 50

Number of cups in Box J at first
= 6 p + 270
= 6 x 50 + 270
= 300 + 270
= 570

Answer(s):570