Peter had three boxes, containing a total of 1100 plastic cups. The number of plastic cups in Box E to the total number of plastic cups was 3 : 11. He sold 409 plastic cups from Box F and sold ¹₅ of the plastic cups in Box G. The number of plastic cups left in Box F to the number of plastic cups left in Box G was 3 : 1. How many plastic cups were there in Box F at first?

	Box E	Box F	Box G	Total
Before	3 u	8 u (800)		11 u (1100)
		12 p + 409	5 p
Change		- 409	- 1 p
			4 p
After		3x4 = 12 p	1x4 = 4 p

11 u = 1100
1 u = 1100 ÷ 11 = 100

Number of plastic cups in Box F and Box G at first
= 8 u
= 8 x 100
= 800

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

12 p + 409 + 5 p = 800
12 p + 5 p = 800 - 409
17 p = 391

1 p = 391 ÷ 17 = 23

Number of cups in Box F at first
= 12 p + 409
= 12 x 23 + 409
= 276 + 409
= 685

Answer(s):685