Wesley had ³₄ as many cards as Liam. Liam had ⁴₇ as many cards as Sabrina. After Wesley and Sabrina gave 26 cards to Liam, Liam had thrice as many cards as Wesley. Sabrina then had the same number of cards as Liam.

1. What was the ratio of the number of cards Sabrina had to the number of cards Wesley had in the beginning? Answer in simplest form.
2. How many cards did Liam have in the end?

Wesley	Liam	Sabrina
3	4
	4	7
3	4	7

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

Ratio of the number of cards that Sabrina had to the number of cards that Wesley had in the beginning = 7 : 3

	Wesley	Liam	Sabrina	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 26	+ 52	- 26
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 Liam received from Wesley and Sabrina
= 2 x 26
= 52

Number of cards that Liam received from Wesley and Sabrina
= 2 x 1 u
= 2 u

2 u = 26

1 u = 26 ÷ 2 = 13

Number of cards that Ashley had in the end
= 6 u
= 6 x 13
= 78