Brandon had ¹₂ as many coins as Daniel. Daniel had ²₃ as many coins as Wendy. After Brandon and Wendy gave 16 coins to Daniel, Daniel had four times as many coins as Brandon. Wendy then had the same number of coins as Daniel.

1. What was the ratio of the number of coins Wendy had to the number of coins Brandon had in the beginning? Answer in simplest form.
2. How many coins did Daniel have in the end?

Brandon	Daniel	Wendy
1	2
	2	3
1	2	3

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

Ratio of the number of coins that Wendy had to the number of coins that Brandon had in the beginning = 3 : 1

	Brandon	Daniel	Wendy	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 16	+ 32	- 16
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of coins at first and in the end remains unchanged. Make the total number of coins the same. LCM of 6 and 9 is 18.

Number of coins that Daniel received from Brandon and Wendy
= 2 x 16
= 32

Number of coins that Daniel received from Brandon and Wendy
= 2 x 1 u
= 2 u

2 u = 16

1 u = 16 ÷ 2 = 8

Number of coins that Ashley had in the end
= 8 u
= 8 x 8
= 64