Mrs Kong had a sum of money. She gave her daughter $2385 and gave ¹₅ of the remaining money to her mother. She used ⁴₅ of the rest of the money on a home theater system and was left with ¹₁₀ of the amount she had at first. What was the sum of money she had at first?

Her daughter	Her mother	Remaining amount		Total
$2385	1x5	4x5
		Home Theater System	Left
		4x4	1x4
9x4 = 36 u			1x4 = 4 u
15 u	5 u	16 u	4 u	40 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 = ¹₁₀ Total amount

Amount that Mrs Kong gave to her daughter
= 36 u - 5 u - 16 u
= 15 u

15 u = 2385

1 u = 2385 ÷ 15 = 159

Total amount that Mrs Kong had at first
= 15 u + 5 u + 16 u + 4 u
= 40 u
= 40 x 159
= $6360

Answer(s): $6360