Mrs Gan had a sum of money. She gave her father $1050 and gave ¹₄ of the remaining money to her daughter. She used ⁴₅ 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 father	Her daughter	Remaining amount		Total
$1050	1x5	3x5
		Dishwasher	Left
		4x3	1x3
9x3 = 27 u			1x3 = 3 u
10 u	5 u	12 u	3 u	30 u

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

The remaining amount is repeated.  Make the remaining amount the same. LCM of 3 and 5 is 15. 

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

¹₅ Remaining amount = ¹₁₀ Total amount

Amount that Mrs Gan gave to her father
= 27 u - 5 u - 12 u
= 10 u

10 u = 1050

1 u = 1050 ÷ 10 = 105

Total amount that Mrs Gan had at first
= 10 u + 5 u + 12 u + 3 u
= 30 u
= 30 x 105
= $3150

Answer(s): $3150