Emma spent some of her money on a vest, a pair of flippers and some rings. She spent ¹₆ of her money and an additional $107 on a vest. Next, she spent ⁴₇ of the remaining money and an additional $47 on a pair of flippers. Finally, she spent ⁴₅ of what she had left on some rings and had $14 left. How much did Emma have at first?
Fraction of the money that she had left
= 1 - ⁴₅ 
= ¹₅

¹₅ of the money she had left = 14
⁵₅ of the money she had left = 5 x 14 = 70

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

³₇ of the remaining money = 70 + 47 = 117
¹₇ of the remaining money = 117 ÷ 3 = 39
⁷₇ of the remaining money = 7 x 39 = 273

Fraction of the total money excluding the additional $107 spent on the vest
= 1 - ¹₆
= ⁵₆

⁵₆ of total money = 273 + 107 = 380
¹₆ of total money = 380 ÷ 5 = 76
⁶₆ of total money = 6 x 76 = 456

Amount that Emma had at first = $456

Answer(s): $456