Owen had ³₄ as many coins as Harry. Harry had ⁴₇ as many coins as Kylie. After Owen and Kylie gave 22 coins to Harry, Harry had thrice as many coins as Owen. Kylie then had the same number of coins as Harry.

1. What was the ratio of the number of coins Owen had to the number of coins Kylie had in the beginning? Answer in simplest form.
2. How many coins did Harry have in the end?

Owen	Harry	Kylie
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Owen had to the number of coins that Kylie had in the beginning = 3 : 7

	Owen	Harry	Kylie	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 coins at first and in the end remains unchanged. Make the total number of coins the same. LCM of 14 and 7 is 14.

Number of coins that Harry received from Owen and Kylie
= 2 x 22
= 44

Number of coins that Harry received from Owen and Kylie
= 2 x 1 u
= 2 u

2 u = 22

1 u = 22 ÷ 2 = 11

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