Mrs Ng had a sum of money. She gave her mother $3297 and gave ¹₆ of the remaining money to her niece. She used ³₄ 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 mother	Her niece	Remaining amount		Total
$3297	1x4	5x4
		Portable Air-conditioner	Left
		3x5	1x5
8x5 = 40 u			1x5 = 5 u
21 u	4 u	15 u	5 u	45 u

Fraction of the remaining amount left 
= 1 - ³₄
= ¹₄

The remaining amount is repeated.  Make the remaining amount the same. LCM of 5 and 4 is 20. 

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

¹₄ Remaining amount = ¹₉ Total amount

Amount that Mrs Ng gave to her mother
= 40 u - 4 u - 15 u
= 21 u

21 u = 3297

1 u = 3297 ÷ 21 = 157

Total amount that Mrs Ng had at first
= 21 u + 4 u + 15 u + 5 u
= 45 u
= 45 x 157
= $7065

Answer(s): $7065