Nicole spent some of her money on a jacket, a pair of shoes and some bracelets. She spent ¹₃ of her money and an additional $165 on a jacket. Next, she spent ³₇ of the remaining money and an additional $45 on a pair of shoes. Finally, she spent ⁴₅ of what she had left on some bracelets and had $11 left. How much did Nicole have at first?
Fraction of the money that she had left
= 1 - ⁴₅ 
= ¹₅

¹₅ of the money she had left = 11
⁵₅ of the money she had left = 5 x 11 = 55

Fraction of the remaining money excluding the additional $45 spent on a pair of shoes
= 1 - ³₇
= ⁴₇

⁴₇ of the remaining money = 55 + 45 = 100
¹₇ of the remaining money = 100 ÷ 4 = 25
⁷₇ of the remaining money = 7 x 25 = 175

Fraction of the total money excluding the additional $165 spent on the jacket
= 1 - ¹₃
= ²₃

²₃ of total money = 175 + 165 = 340
¹₃ of total money = 340 ÷ 2 = 170
³₃ of total money = 3 x 170 = 510

Amount that Nicole had at first = $510

Answer(s): $510