Paul had ³₄ as many coins as Harry. Harry had ⁴₇ as many coins as Jade. After Paul and Jade gave 18 coins to Harry, Harry had thrice as many coins as Paul. Jade then had the same number of coins as Harry.

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

Paul	Harry	Jade
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Jade had to the number of coins that Paul had in the beginning = 7 : 3

	Paul	Harry	Jade	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 18	+ 36	- 18
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 Paul and Jade
= 2 x 18
= 36

Number of coins that Harry received from Paul and Jade
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

Number of coins that Ashley had in the end
= 6 u
= 6 x 9
= 54