Min spent some of her money on a coat, a pair of boots and some bracelets. She spent ¹₃ of her money and an additional $109 on a coat. Next, she spent ⁵₇ of the remaining money and an additional $74 on a pair of boots. Finally, she spent ³₄ of what she had left on some bracelets and had $17 left. How much did Min have at first?
Fraction of the money that she had left
= 1 - ³₄ 
= ¹₄

¹₄ of the money she had left = 17
⁴₄ of the money she had left = 4 x 17 = 68

Fraction of the remaining money excluding the additional $74 spent on a pair of boots
= 1 - ⁵₇
= ²₇

²₇ of the remaining money = 68 + 74 = 142
¹₇ of the remaining money = 142 ÷ 2 = 71
⁷₇ of the remaining money = 7 x 71 = 497

Fraction of the total money excluding the additional $109 spent on the coat
= 1 - ¹₃
= ²₃

²₃ of total money = 497 + 109 = 606
¹₃ of total money = 606 ÷ 2 = 303
³₃ of total money = 3 x 303 = 909

Amount that Min had at first = $909

Answer(s): $909