Min spent some of her money on a dress, a pair of slippers and some necklaces. She spent ¹₃ of her money and an additional $178 on a dress. Next, she spent ⁵₇ of the remaining money and an additional $22 on a pair of slippers. Finally, she spent ⁴₅ of what she had left on some necklaces and had $2 left. How much did Min have at first?
Fraction of the money that she had left
= 1 - ⁴₅ 
= ¹₅

¹₅ of the money she had left = 2
⁵₅ of the money she had left = 5 x 2 = 10

Fraction of the remaining money excluding the additional $22 spent on a pair of slippers
= 1 - ⁵₇
= ²₇

²₇ of the remaining money = 10 + 22 = 32
¹₇ of the remaining money = 32 ÷ 2 = 16
⁷₇ of the remaining money = 7 x 16 = 112

Fraction of the total money excluding the additional $178 spent on the dress
= 1 - ¹₃
= ²₃

²₃ of total money = 112 + 178 = 290
¹₃ of total money = 290 ÷ 2 = 145
³₃ of total money = 3 x 145 = 435

Amount that Min had at first = $435

Answer(s): $435