Owen had three boxes, containing a total of 1000 paper plates. The number of paper plates in Box B to the total number of paper plates was 3 : 10. He sold 457 paper plates from Box C and sold ¹₃ of the paper plates in Box D. The number of paper plates left in Box C to the number of paper plates left in Box D was 3 : 1. How many paper plates were there in Box C at first?

	Box B	Box C	Box D	Total
Before	3 u	7 u (700)		10 u (1000)
		6 p + 457	3 p
Change		- 457	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

10 u = 1000
1 u = 1000 ÷ 10 = 100

Number of paper plates in Box C and Box D at first
= 7 u
= 7 x 100
= 700

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

6 p + 457 + 3 p = 700
6 p + 3 p = 700 - 457
9 p = 243

1 p = 243 ÷ 9 = 27

Number of plates in Box C at first
= 6 p + 457
= 6 x 27 + 457
= 162 + 457
= 619

Answer(s):619