Mrs Yeo had a sum of money. She gave her mother $576 and gave ¹₆ of the remaining money to her nephew. She used ³₄ of the rest of the money on a refrigerator and was left with ¹₆ of the amount she had at first. What was the sum of money she had at first?

Her mother	Her nephew	Remaining amount		Total
$576	1x4	5x4
		Refrigerator	Left
		3x5	1x5
5x5 = 25 u			1x5 = 5 u
6 u	4 u	15 u	5 u	30 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 = ¹₆ Total amount

Amount that Mrs Yeo gave to her mother
= 25 u - 4 u - 15 u
= 6 u

6 u = 576

1 u = 576 ÷ 6 = 96

Total amount that Mrs Yeo had at first
= 6 u + 4 u + 15 u + 5 u
= 30 u
= 30 x 96
= $2880

Answer(s): $2880