Julian had ³₄ as many coins as Fabian. Fabian had ⁴₇ as many coins as Zara. After Julian and Zara gave 10 coins to Fabian, Fabian had thrice as many coins as Julian. Zara then had the same number of coins as Fabian.

1. What was the ratio of the number of coins Zara had to the number of coins Julian had in the beginning? Answer in simplest form.
2. How many coins did Fabian have in the end?

Julian	Fabian	Zara
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Zara had to the number of coins that Julian had in the beginning = 7 : 3

	Julian	Fabian	Zara	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 10	+ 20	- 10
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 Fabian received from Julian and Zara
= 2 x 10
= 20

Number of coins that Fabian received from Julian and Zara
= 2 x 1 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Number of coins that Ashley had in the end
= 6 u
= 6 x 5
= 30