Mrs Sim had a sum of money. She gave her father $1305 and gave ¹₆ of the remaining money to her daughter. She used ⁵₆ of the rest of the money on a portable air-conditioner and was left with ¹₉ of the amount she had at first. What was the sum of money she had at first?

Her father	Her daughter	Remaining amount		Total
$1305	1x6	5x6
		Portable Air-conditioner	Left
		5x5	1x5
8x5 = 40 u			1x5 = 5 u
9 u	6 u	25 u	5 u	45 u

Fraction of the remaining amount left 
= 1 - ⁵₆
= ¹₆

The remaining amount is repeated.  Make the remaining amount the same. LCM of 5 and 6 is 30. 

The amount left is repeated.  Make the amount left the same.

¹₆ Remaining amount = ¹₉ Total amount

Amount that Mrs Sim gave to her father
= 40 u - 6 u - 25 u
= 9 u

9 u = 1305

1 u = 1305 ÷ 9 = 145

Total amount that Mrs Sim had at first
= 9 u + 6 u + 25 u + 5 u
= 45 u
= 45 x 145
= $6525

Answer(s): $6525