Oliver had ³₄ as many cards as Harry. Harry had ⁴₇ as many cards as Sabrina. After Oliver and Sabrina gave 22 cards to Harry, Harry had thrice as many cards as Oliver. Sabrina then had the same number of cards as Harry.

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

Oliver	Harry	Sabrina
3	4
	4	7
3	4	7

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

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

	Oliver	Harry	Sabrina	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 22	+ 44	- 22
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 Harry received from Oliver and Sabrina
= 2 x 22
= 44

Number of cards that Harry received from Oliver and Sabrina
= 2 x 1 u
= 2 u

2 u = 22

1 u = 22 ÷ 2 = 11

Number of cards that Ashley had in the end
= 6 u
= 6 x 11
= 66