Mrs Lin had a sum of money. She gave her nephew $158 and gave ¹₄ of the remaining money to her daughter. She used ³₄ of the rest of the money on a portable air-conditioner and was left with ¹₆ of the amount she had at first. What was the sum of money she had at first?

Her nephew	Her daughter	Remaining amount		Total
$158	1x4	3x4
		Portable Air-conditioner	Left
		3x3	1x3
5x3 = 15 u			1x3 = 3 u
2 u	4 u	9 u	3 u	18 u

Fraction of the remaining amount left 
= 1 - ³₄
= ¹₄

The remaining amount is repeated.  Make the remaining amount the same. LCM of 3 and 4 is 12. 

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

¹₄ Remaining amount = ¹₆ Total amount

Amount that Mrs Lin gave to her nephew
= 15 u - 4 u - 9 u
= 2 u

2 u = 158

1 u = 158 ÷ 2 = 79

Total amount that Mrs Lin had at first
= 2 u + 4 u + 9 u + 3 u
= 18 u
= 18 x 79
= $1422

Answer(s): $1422