Zeph had three boxes, containing a total of 960 plastic cups. The number of plastic cups in Box B to the total number of plastic cups was 3 : 8. He sold 391 plastic cups from Box C and sold ¹₄ of the plastic cups in Box D. The number of plastic cups left in Box C to the number of plastic cups left in Box D was 5 : 1. How many plastic cups were there in Box C at first?

	Box B	Box C	Box D	Total
Before	3 u	5 u (600)		8 u (960)
		15 p + 391	4 p
Change		- 391	- 1 p
			3 p
After		5x3 = 15 p	1x3 = 3 p

8 u = 960
1 u = 960 ÷ 8 = 120

Number of plastic cups in Box C and Box D at first
= 5 u
= 5 x 120
= 600

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

15 p + 391 + 4 p = 600
15 p + 4 p = 600 - 391
19 p = 209

1 p = 209 ÷ 19 = 11

Number of cups in Box C at first
= 15 p + 391
= 15 x 11 + 391
= 165 + 391
= 556

Answer(s):556