George had three boxes, containing a total of 910 styrofoam cups. The number of styrofoam cups in Box H to the total number of styrofoam cups was 3 : 7. He sold 340 styrofoam cups from Box J and sold ¹₃ 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 3 : 1. How many styrofoam cups were there in Box J at first?

	Box H	Box J	Box K	Total
Before	3 u	4 u (520)		7 u (910)
		6 p + 340	3 p
Change		- 340	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

7 u = 910
1 u = 910 ÷ 7 = 130

Number of styrofoam cups in Box J and Box K at first
= 4 u
= 4 x 130
= 520

The number of cups left in K is the repeated identity.
LCM of 1 and 2 = 2

6 p + 340 + 3 p = 520
6 p + 3 p = 520 - 340
9 p = 180

1 p = 180 ÷ 9 = 20

Number of cups in Box J at first
= 6 p + 340
= 6 x 20 + 340
= 120 + 340
= 460

Answer(s):460