John had three boxes, containing a total of 900 plastic bowls. The number of plastic bowls in Box B to the total number of plastic bowls was 3 : 10. He sold 315 plastic bowls from Box C and sold ¹₃ of the plastic bowls in Box D. The number of plastic bowls left in Box C to the number of plastic bowls left in Box D was 3 : 1. How many plastic bowls were there in Box C at first?

	Box B	Box C	Box D	Total
Before	3 u	7 u (630)		10 u (900)
		6 p + 315	3 p
Change		- 315	- 1 p
			2 p
After		3x2 = 6 p	1x2 = 2 p

10 u = 900
1 u = 900 ÷ 10 = 90

Number of plastic bowls in Box C and Box D at first
= 7 u
= 7 x 90
= 630

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

6 p + 315 + 3 p = 630
6 p + 3 p = 630 - 315
9 p = 315

1 p = 315 ÷ 9 = 35

Number of bowls in Box C at first
= 6 p + 315
= 6 x 35 + 315
= 210 + 315
= 525

Answer(s):525