Flynn had three boxes, containing a total of 980 paper cups. The number of paper cups in Box D to the total number of paper cups was 3 : 7. He sold 371 paper cups from Box E and sold ¹₅ of the paper cups in Box F. The number of paper cups left in Box E to the number of paper cups left in Box F was 4 : 1. How many paper cups were there in Box E at first?

	Box D	Box E	Box F	Total
Before	3 u	4 u (560)		7 u (980)
		16 p + 371	5 p
Change		- 371	- 1 p
			4 p
After		4x4 = 16 p	1x4 = 4 p

7 u = 980
1 u = 980 ÷ 7 = 140

Number of paper cups in Box E and Box F at first
= 4 u
= 4 x 140
= 560

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

16 p + 371 + 5 p = 560
16 p + 5 p = 560 - 371
21 p = 189

1 p = 189 ÷ 21 = 9

Number of cups in Box E at first
= 16 p + 371
= 16 x 9 + 371
= 144 + 371
= 515

Answer(s):515