Mrs Lau had a sum of money. She gave her niece $318 and gave ¹₄ of the remaining money to her father. She used ³₄ of the rest of the money on a home theater system and was left with ¹₆ of the amount she had at first. What was the sum of money she had at first?

Her niece	Her father	Remaining amount		Total
$318	1x4	3x4
		Home Theater System	Left
		3x3	1x3
5x3 = 15 u			1x3 = 3 u
2 u	4 u	9 u	3 u	18 u

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

The remaining amount is repeated.  Make the remaining amount the same. LCM of 3 and 4 is 12. 

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

¹₄ Remaining amount = ¹₆ Total amount

Amount that Mrs Lau gave to her niece
= 15 u - 4 u - 9 u
= 2 u

2 u = 318

1 u = 318 ÷ 2 = 159

Total amount that Mrs Lau had at first
= 2 u + 4 u + 9 u + 3 u
= 18 u
= 18 x 159
= $2862

Answer(s): $2862