Daniel had three boxes, containing a total of 800 styrofoam plates. The number of styrofoam plates in Box A to the total number of styrofoam plates was 3 : 8. He sold 398 styrofoam plates from Box B and sold ¹₅ of the styrofoam plates in Box C. The number of styrofoam plates left in Box B to the number of styrofoam plates left in Box C was 3 : 1. How many styrofoam plates were there in Box B at first?

	Box A	Box B	Box C	Total
Before	3 u	5 u (500)		8 u (800)
		12 p + 398	5 p
Change		- 398	- 1 p
			4 p
After		3x4 = 12 p	1x4 = 4 p

8 u = 800
1 u = 800 ÷ 8 = 100

Number of styrofoam plates in Box B and Box C at first
= 5 u
= 5 x 100
= 500

The number of plates left in C is the repeated identity.
LCM of 1 and 4 = 4

12 p + 398 + 5 p = 500
12 p + 5 p = 500 - 398
17 p = 102

1 p = 102 ÷ 17 = 6

Number of plates in Box B at first
= 12 p + 398
= 12 x 6 + 398
= 72 + 398
= 470

Answer(s):470