Mrs Heng had a sum of money. She gave her niece $1424 and gave ¹₆ of the remaining money to her nephew. She used ³₄ of the rest of the money on a washing machine and was left with ¹₈ of the amount she had at first. What was the sum of money she had at first?

Her niece	Her nephew	Remaining amount		Total
$1424	1x4	5x4
		Washing Machine	Left
		3x5	1x5
7x5 = 35 u			1x5 = 5 u
16 u	4 u	15 u	5 u	40 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 = ¹₈ Total amount

Amount that Mrs Heng gave to her niece
= 35 u - 4 u - 15 u
= 16 u

16 u = 1424

1 u = 1424 ÷ 16 = 89

Total amount that Mrs Heng had at first
= 16 u + 4 u + 15 u + 5 u
= 40 u
= 40 x 89
= $3560

Answer(s): $3560