David had three boxes, containing a total of 960 plastic cups. The number of plastic cups in Box H to the total number of plastic cups was 3 : 8. He sold 405 plastic cups from Box J and sold ¹₃ of the plastic cups in Box K. The number of plastic cups left in Box J to the number of plastic cups left in Box K was 5 : 1. How many plastic cups were there in Box J at first?

	Box H	Box J	Box K	Total
Before	3 u	5 u (600)		8 u (960)
		10 p + 405	3 p
Change		- 405	- 1 p
			2 p
After		5x2 = 10 p	1x2 = 2 p

8 u = 960
1 u = 960 ÷ 8 = 120

Number of plastic 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 2 = 2

10 p + 405 + 3 p = 600
10 p + 3 p = 600 - 405
13 p = 195

1 p = 195 ÷ 13 = 15

Number of cups in Box J at first
= 10 p + 405
= 10 x 15 + 405
= 150 + 405
= 555

Answer(s):555