Sarah spent some of her money on a jumpsuit, a pair of sandals and some necklaces. She spent ¹₄ of her money and an additional $216 on a jumpsuit. Next, she spent ⁵₈ of the remaining money and an additional $46 on a pair of sandals. Finally, she spent ⁴₅ of what she had left on some necklaces and had $16 left. How much did Sarah have at first?
Fraction of the money that she had left
= 1 - ⁴₅ 
= ¹₅

¹₅ of the money she had left = 16
⁵₅ of the money she had left = 5 x 16 = 80

Fraction of the remaining money excluding the additional $46 spent on a pair of sandals
= 1 - ⁵₈
= ³₈

³₈ of the remaining money = 80 + 46 = 126
¹₈ of the remaining money = 126 ÷ 3 = 42
⁸₈ of the remaining money = 8 x 42 = 336

Fraction of the total money excluding the additional $216 spent on the jumpsuit
= 1 - ¹₄
= ³₄

³₄ of total money = 336 + 216 = 552
¹₄ of total money = 552 ÷ 3 = 184
⁴₄ of total money = 4 x 184 = 736

Amount that Sarah had at first = $736

Answer(s): $736