Mrs Chen had a sum of money. She gave her niece $2035 and gave ¹₆ of the remaining money to her son. She used ³₄ of the rest of the money on a portable air-conditioner and was left with ¹₇ of the amount she had at first. What was the sum of money she had at first?

Her niece	Her son	Remaining amount		Total
$2035	1x4	5x4
		Portable Air-conditioner	Left
		3x5	1x5
6x5 = 30 u			1x5 = 5 u
11 u	4 u	15 u	5 u	35 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 = ¹₇ Total amount

Amount that Mrs Chen gave to her niece
= 30 u - 4 u - 15 u
= 11 u

11 u = 2035

1 u = 2035 ÷ 11 = 185

Total amount that Mrs Chen had at first
= 11 u + 4 u + 15 u + 5 u
= 35 u
= 35 x 185
= $6475

Answer(s): $6475