Caden had three boxes, containing a total of 700 plastic cups. The number of plastic cups in Box E to the total number of plastic cups was 3 : 7. He sold 348 plastic cups from Box F and sold ¹₃ 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 5 : 1. How many plastic cups were there in Box F at first?

	Box E	Box F	Box G	Total
Before	3 u	4 u (400)		7 u (700)
		10 p + 348	3 p
Change		- 348	- 1 p
			2 p
After		5x2 = 10 p	1x2 = 2 p

7 u = 700
1 u = 700 ÷ 7 = 100

Number of plastic cups in Box F and Box G at first
= 4 u
= 4 x 100
= 400

The number of cups left in G is the repeated identity.
LCM of 1 and 2 = 2

10 p + 348 + 3 p = 400
10 p + 3 p = 400 - 348
13 p = 52

1 p = 52 ÷ 13 = 4

Number of cups in Box F at first
= 10 p + 348
= 10 x 4 + 348
= 40 + 348
= 388

Answer(s):388