Bryan had three boxes, containing a total of 1000 plastic cups. The number of plastic cups in Box D to the total number of plastic cups was 3 : 10. He sold 268 plastic cups from Box E and sold ¹₄ of the plastic cups in Box F. The number of plastic cups left in Box E to the number of plastic cups left in Box F was 4 : 1. How many plastic cups were there in Box E at first?

	Box D	Box E	Box F	Total
Before	3 u	7 u (700)		10 u (1000)
		12 p + 268	4 p
Change		- 268	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

10 u = 1000
1 u = 1000 ÷ 10 = 100

Number of plastic cups in Box E and Box F at first
= 7 u
= 7 x 100
= 700

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

12 p + 268 + 4 p = 700
12 p + 4 p = 700 - 268
16 p = 432

1 p = 432 ÷ 16 = 27

Number of cups in Box E at first
= 12 p + 268
= 12 x 27 + 268
= 324 + 268
= 592

Answer(s):592