Justin had ³₄ as many coins as Reggie. Reggie had ⁴₇ as many coins as Yoko. After Justin and Yoko gave 28 coins to Reggie, Reggie had thrice as many coins as Justin. Yoko then had the same number of coins as Reggie.

1. What was the ratio of the number of coins Yoko had to the number of coins Justin had in the beginning? Answer in simplest form.
2. How many coins did Reggie have in the end?

Justin	Reggie	Yoko
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Yoko had to the number of coins that Justin had in the beginning = 7 : 3

	Justin	Reggie	Yoko	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 28	+ 56	- 28
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 Reggie received from Justin and Yoko
= 2 x 28
= 56

Number of coins that Reggie received from Justin and Yoko
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of coins that Ashley had in the end
= 6 u
= 6 x 14
= 84