Mrs Lim gave Barbara and Ivory some money each on Monday. On Tuesday, Barbara gave ¹₃ of the amount she had to Ivory. On Wednesday, Ivory gave ¹₄ of the amount she had to Barbara. In the end, Barbara had $22 and Ivory had $12. How much did Ivory had more than Barbara at first?

	Barbara	Ivory	Total
Before 1	3 u	?	$34
Change 1	- 1 u	+ 1 u
After 1	2 u	4 p	$34
Before 2	$22 - 1 p	4 p	$34
Change 2	+ 1 p	- 1 p
After 2	$22	3 p ($12)	$34

Amount that Ivory had in the end = 3 p

3 p = 12

1 p = 12 ÷ 3 = 4

Working backwards.

Amount that Barbara had after giving to Ivory on Tuesday
= 22 - 1 p
= 22 - 4
= $18

2 u = 18

1 u = 18 ÷ 2 = 9

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

Total amount that Barbara and Ivory had 
= 22 + 12
= $34

Amount that Ivory had at first
= 34 - 27
= $7

Amount that Barbara had more than Ivory
= 27 - 7 
= $20

Answer(s): $20