Mrs Thia had a sum of money. She gave her mother $192 and gave ¹₅ of the remaining money to her daughter. She used ⁵₆ 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 mother	Her daughter	Remaining amount		Total
$192	1x3	4x3
		Home Theater System	Left
		5x2	1x2
8x2 = 16 u			1x2 = 2 u
3 u	3 u	10 u	2 u	18 u

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

The remaining amount is repeated.  Make the remaining amount the same. LCM of 4 and 6 is 12. 

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

¹₆ Remaining amount = ¹₉ Total amount

Amount that Mrs Thia gave to her mother
= 16 u - 3 u - 10 u
= 3 u

3 u = 192

1 u = 192 ÷ 3 = 64

Total amount that Mrs Thia had at first
= 3 u + 3 u + 10 u + 2 u
= 18 u
= 18 x 64
= $1152

Answer(s): $1152