Anna spent some of her money on a sweater, a pair of floaters and some necklaces. She spent ¹₄ of her money and an additional $171 on a sweater. Next, she spent ²₅ of the remaining money and an additional $30 on a pair of floaters. Finally, she spent ²₃ of what she had left on some necklaces and had $14 left. How much did Anna have at first?
Fraction of the money that she had left
= 1 - ²₃ 
= ¹₃

¹₃ of the money she had left = 14
³₃ of the money she had left = 3 x 14 = 42

Fraction of the remaining money excluding the additional $30 spent on a pair of floaters
= 1 - ²₅
= ³₅

³₅ of the remaining money = 42 + 30 = 72
¹₅ of the remaining money = 72 ÷ 3 = 24
⁵₅ of the remaining money = 5 x 24 = 120

Fraction of the total money excluding the additional $171 spent on the sweater
= 1 - ¹₄
= ³₄

³₄ of total money = 120 + 171 = 291
¹₄ of total money = 291 ÷ 3 = 97
⁴₄ of total money = 4 x 97 = 388

Amount that Anna had at first = $388

Answer(s): $388