Elyse spent some of her money on a blazer, a pair of sandals and some bracelets. She spent ¹₃ of her money and an additional $167 on a blazer. Next, she spent ³₇ of the remaining money and an additional $51 on a pair of sandals. Finally, she spent ²₃ of what she had left on some bracelets and had $11 left. How much did Elyse have at first?
Fraction of the money that she had left
= 1 - ²₃ 
= ¹₃

¹₃ of the money she had left = 11
³₃ of the money she had left = 3 x 11 = 33

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

⁴₇ of the remaining money = 33 + 51 = 84
¹₇ of the remaining money = 84 ÷ 4 = 21
⁷₇ of the remaining money = 7 x 21 = 147

Fraction of the total money excluding the additional $167 spent on the blazer
= 1 - ¹₃
= ²₃

²₃ of total money = 147 + 167 = 314
¹₃ of total money = 314 ÷ 2 = 157
³₃ of total money = 3 x 157 = 471

Amount that Elyse had at first = $471

Answer(s): $471