Diana spent some of her money on a jacket, a pair of shoes and some necklaces. She spent ¹₈ of her money and an additional $249 on a jacket. Next, she spent ²₅ of the remaining money and an additional $51 on a pair of shoes. Finally, she spent ⁴₅ of what she had left on some necklaces and had $12 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 = 12
⁵₅ of the money she had left = 5 x 12 = 60

Fraction of the remaining money excluding the additional $51 spent on a pair of shoes
= 1 - ²₅
= ³₅

³₅ of the remaining money = 60 + 51 = 111
¹₅ of the remaining money = 111 ÷ 3 = 37
⁵₅ of the remaining money = 5 x 37 = 185

Fraction of the total money excluding the additional $249 spent on the jacket
= 1 - ¹₈
= ⁷₈

⁷₈ of total money = 185 + 249 = 434
¹₈ of total money = 434 ÷ 7 = 62
⁸₈ of total money = 8 x 62 = 496

Amount that Diana had at first = $496

Answer(s): $496