Rachel spent some of her money on a coat, a pair of trainers and some bracelets. She spent ¹₃ of her money and an additional $290 on a coat. Next, she spent ³₅ of the remaining money and an additional $86 on a pair of trainers. Finally, she spent ⁵₆ of what she had left on some bracelets and had $13 left. How much did Rachel have at first?
Fraction of the money that she had left
= 1 - ⁵₆ 
= ¹₆

¹₆ of the money she had left = 13
⁶₆ of the money she had left = 6 x 13 = 78

Fraction of the remaining money excluding the additional $86 spent on a pair of trainers
= 1 - ³₅
= ²₅

²₅ of the remaining money = 78 + 86 = 164
¹₅ of the remaining money = 164 ÷ 2 = 82
⁵₅ of the remaining money = 5 x 82 = 410

Fraction of the total money excluding the additional $290 spent on the coat
= 1 - ¹₃
= ²₃

²₃ of total money = 410 + 290 = 700
¹₃ of total money = 700 ÷ 2 = 350
³₃ of total money = 3 x 350 = 1050

Amount that Rachel had at first = $1050

Answer(s): $1050