Mrs Fong had a sum of money. She gave her nephew $369 and gave ¹₃ of the remaining money to her son. She used ⁴₅ of the rest of the money on a portable air-conditioner and was left with ¹₉ of the amount she had at first. What was the sum of money she had at first?

Her nephew	Her son	Remaining amount		Total
$369	1x5	2x5
		Portable Air-conditioner	Left
		4x2	1x2
8x2 = 16 u			1x2 = 2 u
3 u	5 u	8 u	2 u	18 u

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

The remaining amount is repeated.  Make the remaining amount the same. LCM of 2 and 5 is 10. 

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

¹₅ Remaining amount = ¹₉ Total amount

Amount that Mrs Fong gave to her nephew
= 16 u - 5 u - 8 u
= 3 u

3 u = 369

1 u = 369 ÷ 3 = 123

Total amount that Mrs Fong had at first
= 3 u + 5 u + 8 u + 2 u
= 18 u
= 18 x 123
= $2214

Answer(s): $2214