Diana spent some of her money on a dress, a pair of ballet shoes and some rings. She spent ¹₆ of her money and an additional $292 on a dress. Next, she spent ²₇ of the remaining money and an additional $90 on a pair of ballet shoes. Finally, she spent ⁴₅ of what she had left on some rings and had $16 left. How much did Diana 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 $90 spent on a pair of ballet shoes
= 1 - ²₇
= ⁵₇

⁵₇ of the remaining money = 80 + 90 = 170
¹₇ of the remaining money = 170 ÷ 5 = 34
⁷₇ of the remaining money = 7 x 34 = 238

Fraction of the total money excluding the additional $292 spent on the dress
= 1 - ¹₆
= ⁵₆

⁵₆ of total money = 238 + 292 = 530
¹₆ of total money = 530 ÷ 5 = 106
⁶₆ of total money = 6 x 106 = 636

Amount that Diana had at first = $636

Answer(s): $636