Raeann spent some of her money on a coat, a pair of sandals and some bracelets. She spent ¹₄ of her money and an additional $193 on a coat. Next, she spent ²₅ of the remaining money and an additional $30 on a pair of sandals. Finally, she spent ⁴₅ of what she had left on some bracelets and had $9 left. How much did Raeann have at first?
Fraction of the money that she had left
= 1 - ⁴₅ 
= ¹₅

¹₅ of the money she had left = 9
⁵₅ of the money she had left = 5 x 9 = 45

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

³₅ of the remaining money = 45 + 30 = 75
¹₅ of the remaining money = 75 ÷ 3 = 25
⁵₅ of the remaining money = 5 x 25 = 125

Fraction of the total money excluding the additional $193 spent on the coat
= 1 - ¹₄
= ³₄

³₄ of total money = 125 + 193 = 318
¹₄ of total money = 318 ÷ 3 = 106
⁴₄ of total money = 4 x 106 = 424

Amount that Raeann had at first = $424

Answer(s): $424