Dylan had ³₄ as many cards as Cole. Cole had ⁴₇ as many cards as Raeann. After Dylan and Raeann gave 30 cards to Cole, Cole had thrice as many cards as Dylan. Raeann then had the same number of cards as Cole.

1. What was the ratio of the number of cards Dylan had to the number of cards Raeann had in the beginning? Answer in simplest form.
2. How many cards did Cole have in the end?

Dylan	Cole	Raeann
3	4
	4	7
3	4	7

(a)
The number of cards that Cole is repeated.  

Ratio of the number of cards that Dylan had to the number of cards that Raeann had in the beginning = 3 : 7

	Dylan	Cole	Raeann	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 30	+ 60	- 30
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of cards at first and in the end remains unchanged. Make the total number of cards the same. LCM of 14 and 7 is 14.

Number of cards that Cole received from Dylan and Raeann
= 2 x 30
= 60

Number of cards that Cole received from Dylan and Raeann
= 2 x 1 u
= 2 u

2 u = 30

1 u = 30 ÷ 2 = 15

Number of cards that Ashley had in the end
= 6 u
= 6 x 15
= 90