Mrs Teo had a sum of money. She gave her nephew $725 and gave ¹₅ of the remaining money to her father. 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 father	Remaining amount		Total
$725	1x3	4x3
		Dishwasher	Left
		5x2	1x2
9x2 = 18 u			1x2 = 2 u
5 u	3 u	10 u	2 u	20 u

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

The remaining amount is repeated.  Make the remaining amount the same. LCM of 4 and 6 is 12. 

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

¹₆ Remaining amount = ¹₁₀ Total amount

Amount that Mrs Teo gave to her nephew
= 18 u - 3 u - 10 u
= 5 u

5 u = 725

1 u = 725 ÷ 5 = 145

Total amount that Mrs Teo had at first
= 5 u + 3 u + 10 u + 2 u
= 20 u
= 20 x 145
= $2900

Answer(s): $2900