Mrs Lin had a sum of money. She gave her mother $2704 and gave ¹₆ of the remaining money to her father. She used ³₄ of the rest of the money on a refrigerator and was left with ¹₈ of the amount she had at first. What was the sum of money she had at first?

Her mother	Her father	Remaining amount		Total
$2704	1x4	5x4
		Refrigerator	Left
		3x5	1x5
7x5 = 35 u			1x5 = 5 u
16 u	4 u	15 u	5 u	40 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 = ¹₈ Total amount

Amount that Mrs Lin gave to her mother
= 35 u - 4 u - 15 u
= 16 u

16 u = 2704

1 u = 2704 ÷ 16 = 169

Total amount that Mrs Lin had at first
= 16 u + 4 u + 15 u + 5 u
= 40 u
= 40 x 169
= $6760

Answer(s): $6760