Mrs Zhang gave Dana and Natalie some money each on Tuesday. On Wednesday, Dana gave ¹₅ of the amount she had to Natalie. On Thursday, Natalie gave ¹₃ of the amount she had to Dana. In the end, Dana had $53 and Natalie had $18. How much did Natalie had more than Dana at first?

	Dana	Natalie	Total
Before 1	5 u	?	$71
Change 1	- 1 u	+ 1 u
After 1	4 u	3 p	$71
Before 2	$53 - 1 p	3 p	$71
Change 2	+ 1 p	- 1 p
After 2	$53	2 p ($18)	$71

Amount that Natalie had in the end = 2 p

2 p = 18

1 p = 18 ÷ 2 = 9

Working backwards.

Amount that Dana had after giving to Natalie on Wednesday
= 53 - 1 p
= 53 - 9
= $44

4 u = 44

1 u = 44 ÷ 4 = 11

Amount that Dana had at first
= 5 u
= 5 x 11
= $55

Total amount that Dana and Natalie had 
= 53 + 18
= $71

Amount that Natalie had at first
= 71 - 55
= $16

Amount that Dana had more than Natalie
= 55 - 16 
= $39

Answer(s): $39