Mrs Ng had a sum of money. She gave her nephew $2352 and gave ¹₆ of the remaining money to her mother. She used ⁵₆ of the rest of the money on a dishwasher and was left with ¹₁₀ of the amount she had at first. What was the sum of money she had at first?

Her nephew	Her mother	Remaining amount		Total
$2352	1x6	5x6
		Dishwasher	Left
		5x5	1x5
9x5 = 45 u			1x5 = 5 u
14 u	6 u	25 u	5 u	50 u

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

The remaining amount is repeated.  Make the remaining amount the same. LCM of 5 and 6 is 30. 

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

¹₆ Remaining amount = ¹₁₀ Total amount

Amount that Mrs Ng gave to her nephew
= 45 u - 6 u - 25 u
= 14 u

14 u = 2352

1 u = 2352 ÷ 14 = 168

Total amount that Mrs Ng had at first
= 14 u + 6 u + 25 u + 5 u
= 50 u
= 50 x 168
= $8400

Answer(s): $8400