Mrs Ong had a sum of money. She gave her niece $564 and gave ¹₃ of the remaining money to her mother. She used ⁴₅ of the rest of the money on a washing machine and was left with ¹₉ of the amount she had at first. What was the sum of money she had at first?

Her niece	Her mother	Remaining amount		Total
$564	1x5	2x5
		Washing Machine	Left
		4x2	1x2
8x2 = 16 u			1x2 = 2 u
3 u	5 u	8 u	2 u	18 u

Fraction of the remaining amount left 
= 1 - ⁴₅
= ¹₅

The remaining amount is repeated.  Make the remaining amount the same. LCM of 2 and 5 is 10. 

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

¹₅ Remaining amount = ¹₉ Total amount

Amount that Mrs Ong gave to her niece
= 16 u - 5 u - 8 u
= 3 u

3 u = 564

1 u = 564 ÷ 3 = 188

Total amount that Mrs Ong had at first
= 3 u + 5 u + 8 u + 2 u
= 18 u
= 18 x 188
= $3384

Answer(s): $3384