Bobby had ³₄ as many coins as Harry. Harry had ⁴₇ as many coins as Emma. After Bobby and Emma gave 8 coins to Harry, Harry had thrice as many coins as Bobby. Emma then had the same number of coins as Harry.

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

Bobby	Harry	Emma
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Emma had to the number of coins that Bobby had in the beginning = 7 : 3

	Bobby	Harry	Emma	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 8	+ 16	- 8
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 Bobby and Emma
= 2 x 8
= 16

Number of coins that Harry received from Bobby and Emma
= 2 x 1 u
= 2 u

2 u = 8

1 u = 8 ÷ 2 = 4

Number of coins that Ashley had in the end
= 6 u
= 6 x 4
= 24