Xandra spent some of her money on a coat, a pair of trainers and some bracelets. She spent ¹₄ of her money and an additional $157 on a coat. Next, she spent ⁴₇ of the remaining money and an additional $50 on a pair of trainers. Finally, she spent ⁴₅ of what she had left on some bracelets and had $20 left. How much did Xandra have at first?
Fraction of the money that she had left
= 1 - ⁴₅ 
= ¹₅

¹₅ of the money she had left = 20
⁵₅ of the money she had left = 5 x 20 = 100

Fraction of the remaining money excluding the additional $50 spent on a pair of trainers
= 1 - ⁴₇
= ³₇

³₇ of the remaining money = 100 + 50 = 150
¹₇ of the remaining money = 150 ÷ 3 = 50
⁷₇ of the remaining money = 7 x 50 = 350

Fraction of the total money excluding the additional $157 spent on the coat
= 1 - ¹₄
= ³₄

³₄ of total money = 350 + 157 = 507
¹₄ of total money = 507 ÷ 3 = 169
⁴₄ of total money = 4 x 169 = 676

Amount that Xandra had at first = $676

Answer(s): $676