Mrs Yee had a sum of money. She gave her mother $315 and gave ¹₅ of the remaining money to her daughter. She used ⁴₅ of the rest of the money on a dishwasher and was left with ¹₇ of the amount she had at first. What was the sum of money she had at first?

Her mother	Her daughter	Remaining amount		Total
$315	1x5	4x5
		Dishwasher	Left
		4x4	1x4
6x4 = 24 u			1x4 = 4 u
3 u	5 u	16 u	4 u	28 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 = ¹₇ Total amount

Amount that Mrs Yee gave to her mother
= 24 u - 5 u - 16 u
= 3 u

3 u = 315

1 u = 315 ÷ 3 = 105

Total amount that Mrs Yee had at first
= 3 u + 5 u + 16 u + 4 u
= 28 u
= 28 x 105
= $2940

Answer(s): $2940