Mrs Lim gave Dana and Kimberly some money each on Monday. On Tuesday, Dana gave ¹₃ of the amount she had to Kimberly. On Wednesday, Kimberly gave ¹₅ of the amount she had to Dana. In the end, Dana had $20 and Kimberly had $8. How much did Kimberly had more than Dana at first?

	Dana	Kimberly	Total
Before 1	3 u	?	$28
Change 1	- 1 u	+ 1 u
After 1	2 u	5 p	$28
Before 2	$20 - 1 p	5 p	$28
Change 2	+ 1 p	- 1 p
After 2	$20	4 p ($8)	$28

Amount that Kimberly had in the end = 4 p

4 p = 8

1 p = 8 ÷ 4 = 2

Working backwards.

Amount that Dana had after giving to Kimberly on Tuesday
= 20 - 1 p
= 20 - 2
= $18

2 u = 18

1 u = 18 ÷ 2 = 9

Amount that Dana had at first
= 3 u
= 3 x 9
= $27

Total amount that Dana and Kimberly had 
= 20 + 8
= $28

Amount that Kimberly had at first
= 28 - 27
= $1

Amount that Dana had more than Kimberly
= 27 - 1 
= $26

Answer(s): $26