Lee had three boxes, containing a total of 1540 paper cups. The number of paper cups in Box H to the total number of paper cups was 3 : 11. He sold 445 paper cups from Box J and sold ¹₅ of the paper cups in Box K. The number of paper cups left in Box J to the number of paper cups left in Box K was 5 : 1. How many paper cups were there in Box J at first?

	Box H	Box J	Box K	Total
Before	3 u	8 u (1120)		11 u (1540)
		20 p + 445	5 p
Change		- 445	- 1 p
			4 p
After		5x4 = 20 p	1x4 = 4 p

11 u = 1540
1 u = 1540 ÷ 11 = 140

Number of paper cups in Box J and Box K at first
= 8 u
= 8 x 140
= 1120

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

20 p + 445 + 5 p = 1120
20 p + 5 p = 1120 - 445
25 p = 675

1 p = 675 ÷ 25 = 27

Number of cups in Box J at first
= 20 p + 445
= 20 x 27 + 445
= 540 + 445
= 985

Answer(s):985