Mary spent some of her money on a vest, a pair of shoes and some rings. She spent ¹₅ of her money and an additional $241 on a vest. Next, she spent ²₇ of the remaining money and an additional $37 on a pair of shoes. Finally, she spent ³₄ of what she had left on some rings and had $7 left. How much did Mary have at first?
Fraction of the money that she had left
= 1 - ³₄ 
= ¹₄

¹₄ of the money she had left = 7
⁴₄ of the money she had left = 4 x 7 = 28

Fraction of the remaining money excluding the additional $37 spent on a pair of shoes
= 1 - ²₇
= ⁵₇

⁵₇ of the remaining money = 28 + 37 = 65
¹₇ of the remaining money = 65 ÷ 5 = 13
⁷₇ of the remaining money = 7 x 13 = 91

Fraction of the total money excluding the additional $241 spent on the vest
= 1 - ¹₅
= ⁴₅

⁴₅ of total money = 91 + 241 = 332
¹₅ of total money = 332 ÷ 4 = 83
⁵₅ of total money = 5 x 83 = 415

Amount that Mary had at first = $415

Answer(s): $415