Mrs Loh had a sum of money. She gave her daughter $973 and gave ¹₅ of the remaining money to her niece. She used ⁴₅ of the rest of the money on a portable air-conditioner and was left with ¹₈ of the amount she had at first. What was the sum of money she had at first?

Her daughter	Her niece	Remaining amount		Total
$973	1x5	4x5
		Portable Air-conditioner	Left
		4x4	1x4
7x4 = 28 u			1x4 = 4 u
7 u	5 u	16 u	4 u	32 u

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

The remaining amount is repeated.  Make the remaining amount the same. LCM of 4 and 5 is 20. 

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

¹₅ Remaining amount = ¹₈ Total amount

Amount that Mrs Loh gave to her daughter
= 28 u - 5 u - 16 u
= 7 u

7 u = 973

1 u = 973 ÷ 7 = 139

Total amount that Mrs Loh had at first
= 7 u + 5 u + 16 u + 4 u
= 32 u
= 32 x 139
= $4448

Answer(s): $4448