Mrs Ng gave Diana and Penelope some money each on Tuesday. On Wednesday, Diana gave ¹₄ of the amount she had to Penelope. On Thursday, Penelope gave ¹₃ of the amount she had to Diana. In the end, Diana had $18 and Penelope had $6. How much did Penelope had more than Diana at first?

	Diana	Penelope	Total
Before 1	4 u	?	$24
Change 1	- 1 u	+ 1 u
After 1	3 u	3 p	$24
Before 2	$18 - 1 p	3 p	$24
Change 2	+ 1 p	- 1 p
After 2	$18	2 p ($6)	$24

Amount that Penelope had in the end = 2 p

2 p = 6

1 p = 6 ÷ 2 = 3

Working backwards.

Amount that Diana had after giving to Penelope on Wednesday
= 18 - 1 p
= 18 - 3
= $15

3 u = 15

1 u = 15 ÷ 3 = 5

Amount that Diana had at first
= 4 u
= 4 x 5
= $20

Total amount that Diana and Penelope had 
= 18 + 6
= $24

Amount that Penelope had at first
= 24 - 20
= $4

Amount that Diana had more than Penelope
= 20 - 4 
= $16

Answer(s): $16