Howard had three boxes, containing a total of 910 styrofoam plates. The number of styrofoam plates in Box G to the total number of styrofoam plates was 3 : 7. He sold 408 styrofoam plates from Box H and sold ¹₄ of the styrofoam plates in Box J. The number of styrofoam plates left in Box H to the number of styrofoam plates left in Box J was 4 : 1. How many styrofoam plates were there in Box H at first?

	Box G	Box H	Box J	Total
Before	3 u	4 u (520)		7 u (910)
		12 p + 408	4 p
Change		- 408	- 1 p
			3 p
After		4x3 = 12 p	1x3 = 3 p

7 u = 910
1 u = 910 ÷ 7 = 130

Number of styrofoam plates in Box H and Box J at first
= 4 u
= 4 x 130
= 520

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

12 p + 408 + 4 p = 520
12 p + 4 p = 520 - 408
16 p = 112

1 p = 112 ÷ 16 = 7

Number of plates in Box H at first
= 12 p + 408
= 12 x 7 + 408
= 84 + 408
= 492

Answer(s):492