Riordan had three boxes, containing a total of 440 plastic cups. The number of plastic cups in Box J to the total number of plastic cups was 3 : 11. He sold 263 plastic cups from Box K and sold ¹₄ of the plastic cups in Box L. The number of plastic cups left in Box K to the number of plastic cups left in Box L was 5 : 1. How many plastic cups were there in Box K at first?

	Box J	Box K	Box L	Total
Before	3 u	8 u (320)		11 u (440)
		15 p + 263	4 p
Change		- 263	- 1 p
			3 p
After		5x3 = 15 p	1x3 = 3 p

11 u = 440
1 u = 440 ÷ 11 = 40

Number of plastic cups in Box K and Box L at first
= 8 u
= 8 x 40
= 320

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

15 p + 263 + 4 p = 320
15 p + 4 p = 320 - 263
19 p = 57

1 p = 57 ÷ 19 = 3

Number of cups in Box K at first
= 15 p + 263
= 15 x 3 + 263
= 45 + 263
= 308

Answer(s):308