Seth had three boxes, containing a total of 880 styrofoam plates. The number of styrofoam plates in Box E to the total number of styrofoam plates was 3 : 8. He sold 251 styrofoam plates from Box F and sold ¹₄ of the styrofoam plates in Box G. The number of styrofoam plates left in Box F to the number of styrofoam plates left in Box G was 3 : 1. How many styrofoam plates were there in Box F at first?

	Box E	Box F	Box G	Total
Before	3 u	5 u (550)		8 u (880)
		9 p + 251	4 p
Change		- 251	- 1 p
			3 p
After		3x3 = 9 p	1x3 = 3 p

8 u = 880
1 u = 880 ÷ 8 = 110

Number of styrofoam plates in Box F and Box G at first
= 5 u
= 5 x 110
= 550

The number of plates left in G is the repeated identity.
LCM of 1 and 3 = 3

9 p + 251 + 4 p = 550
9 p + 4 p = 550 - 251
13 p = 299

1 p = 299 ÷ 13 = 23

Number of plates in Box F at first
= 9 p + 251
= 9 x 23 + 251
= 207 + 251
= 458

Answer(s):458