Ian had ³₄ as many cards as Julian. Julian had ⁴₇ as many cards as Xandra. After Ian and Xandra gave 28 cards to Julian, Julian had thrice as many cards as Ian. Xandra then had the same number of cards as Julian.

1. What was the ratio of the number of cards Xandra had to the number of cards Ian had in the beginning? Answer in simplest form.
2. How many cards did Julian have in the end?

Ian	Julian	Xandra
3	4
	4	7
3	4	7

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

Ratio of the number of cards that Xandra had to the number of cards that Ian had in the beginning = 7 : 3

	Ian	Julian	Xandra	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 28	+ 56	- 28
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 Julian received from Ian and Xandra
= 2 x 28
= 56

Number of cards that Julian received from Ian and Xandra
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of cards that Ashley had in the end
= 6 u
= 6 x 14
= 84