Mrs Oh had a sum of money. She gave her son $3874 and gave ¹₆ of the remaining money to her daughter. She used ³₄ of the rest of the money on a dishwasher and was left with ¹₁₀ of the amount she had at first. What was the sum of money she had at first?

Her son	Her daughter	Remaining amount		Total
$3874	1x4	5x4
		Dishwasher	Left
		3x5	1x5
9x5 = 45 u			1x5 = 5 u
26 u	4 u	15 u	5 u	50 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 = ¹₁₀ Total amount

Amount that Mrs Oh gave to her son
= 45 u - 4 u - 15 u
= 26 u

26 u = 3874

1 u = 3874 ÷ 26 = 149

Total amount that Mrs Oh had at first
= 26 u + 4 u + 15 u + 5 u
= 50 u
= 50 x 149
= $7450

Answer(s): $7450