Irene spent some of her money on a dress, a pair of trainers and some necklaces. She spent ¹₄ of her money and an additional $261 on a dress. Next, she spent ³₅ of the remaining money and an additional $46 on a pair of trainers. Finally, she spent ³₄ of what she had left on some necklaces and had $8 left. How much did Irene have at first?
Fraction of the money that she had left
= 1 - ³₄ 
= ¹₄

¹₄ of the money she had left = 8
⁴₄ of the money she had left = 4 x 8 = 32

Fraction of the remaining money excluding the additional $46 spent on a pair of trainers
= 1 - ³₅
= ²₅

²₅ of the remaining money = 32 + 46 = 78
¹₅ of the remaining money = 78 ÷ 2 = 39
⁵₅ of the remaining money = 5 x 39 = 195

Fraction of the total money excluding the additional $261 spent on the dress
= 1 - ¹₄
= ³₄

³₄ of total money = 195 + 261 = 456
¹₄ of total money = 456 ÷ 3 = 152
⁴₄ of total money = 4 x 152 = 608

Amount that Irene had at first = $608

Answer(s): $608