Mrs Ong had a sum of money. She gave her son $1029 and gave ¹₄ of the remaining money to her niece. She used ⁴₅ of the rest of the money on a home theater system and was left with ¹₉ of the amount she had at first. What was the sum of money she had at first?

Her son	Her niece	Remaining amount		Total
$1029	1x5	3x5
		Home Theater System	Left
		4x3	1x3
8x3 = 24 u			1x3 = 3 u
7 u	5 u	12 u	3 u	27 u

Fraction of the remaining amount left 
= 1 - ⁴₅
= ¹₅

The remaining amount is repeated.  Make the remaining amount the same. LCM of 3 and 5 is 15. 

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

¹₅ Remaining amount = ¹₉ Total amount

Amount that Mrs Ong gave to her son
= 24 u - 5 u - 12 u
= 7 u

7 u = 1029

1 u = 1029 ÷ 7 = 147

Total amount that Mrs Ong had at first
= 7 u + 5 u + 12 u + 3 u
= 27 u
= 27 x 147
= $3969

Answer(s): $3969