Bryan had three boxes, containing a total of 1320 styrofoam plates. The number of styrofoam plates in Box B to the total number of styrofoam plates was 3 : 11. He sold 267 styrofoam plates from Box C and sold ¹₃ of the styrofoam plates in Box D. The number of styrofoam plates left in Box C to the number of styrofoam plates left in Box D was 3 : 1. How many styrofoam plates were there in Box C at first?

	Box B	Box C	Box D	Total
Before	3 u	8 u (960)		11 u (1320)
		6 p + 267	3 p
Change		- 267	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

11 u = 1320
1 u = 1320 ÷ 11 = 120

Number of styrofoam plates in Box C and Box D at first
= 8 u
= 8 x 120
= 960

The number of plates left in D is the repeated identity.
LCM of 1 and 2 = 2

6 p + 267 + 3 p = 960
6 p + 3 p = 960 - 267
9 p = 693

1 p = 693 ÷ 9 = 77

Number of plates in Box C at first
= 6 p + 267
= 6 x 77 + 267
= 462 + 267
= 729

Answer(s):729