Mrs Ma had a sum of money. She gave her daughter $3486 and gave ¹₆ of the remaining money to her niece. She used ³₄ of the rest of the money on a laptop and was left with ¹₉ of the amount she had at first. What was the sum of money she had at first?

Her daughter	Her niece	Remaining amount		Total
$3486	1x4	5x4
		Laptop	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 Ma gave to her daughter
= 40 u - 4 u - 15 u
= 21 u

21 u = 3486

1 u = 3486 ÷ 21 = 166

Total amount that Mrs Ma had at first
= 21 u + 4 u + 15 u + 5 u
= 45 u
= 45 x 166
= $7470

Answer(s): $7470