Jen spent some of her money on a vest, a pair of sport shoes and some bracelets. She spent ¹₃ of her money and an additional $175 on a vest. Next, she spent ⁴₇ of the remaining money and an additional $51 on a pair of sport shoes. Finally, she spent ²₃ of what she had left on some bracelets and had $2 left. How much did Jen have at first?
Fraction of the money that she had left
= 1 - ²₃ 
= ¹₃

¹₃ of the money she had left = 2
³₃ of the money she had left = 3 x 2 = 6

Fraction of the remaining money excluding the additional $51 spent on a pair of sport shoes
= 1 - ⁴₇
= ³₇

³₇ of the remaining money = 6 + 51 = 57
¹₇ of the remaining money = 57 ÷ 3 = 19
⁷₇ of the remaining money = 7 x 19 = 133

Fraction of the total money excluding the additional $175 spent on the vest
= 1 - ¹₃
= ²₃

²₃ of total money = 133 + 175 = 308
¹₃ of total money = 308 ÷ 2 = 154
³₃ of total money = 3 x 154 = 462

Amount that Jen had at first = $462

Answer(s): $462