Mrs Lu had a sum of money. She gave her nephew $1716 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 ¹₉ of the amount she had at first. What was the sum of money she had at first?

Her nephew	Her father	Remaining amount		Total
$1716	1x4	3x4
		Home Theater System	Left
		3x3	1x3
8x3 = 24 u			1x3 = 3 u
11 u	4 u	9 u	3 u	27 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 = ¹₉ Total amount

Amount that Mrs Lu gave to her nephew
= 24 u - 4 u - 9 u
= 11 u

11 u = 1716

1 u = 1716 ÷ 11 = 156

Total amount that Mrs Lu had at first
= 11 u + 4 u + 9 u + 3 u
= 27 u
= 27 x 156
= $4212

Answer(s): $4212