Gem spent some of her money on a skirt, a pair of floaters and some bracelets. She spent ¹₃ of her money and an additional $180 on a skirt. Next, she spent ²₅ of the remaining money and an additional $74 on a pair of floaters. Finally, she spent ³₄ of what she had left on some bracelets and had $13 left. How much did Gem have at first?
Fraction of the money that she had left
= 1 - ³₄ 
= ¹₄

¹₄ of the money she had left = 13
⁴₄ of the money she had left = 4 x 13 = 52

Fraction of the remaining money excluding the additional $74 spent on a pair of floaters
= 1 - ²₅
= ³₅

³₅ of the remaining money = 52 + 74 = 126
¹₅ of the remaining money = 126 ÷ 3 = 42
⁵₅ of the remaining money = 5 x 42 = 210

Fraction of the total money excluding the additional $180 spent on the skirt
= 1 - ¹₃
= ²₃

²₃ of total money = 210 + 180 = 390
¹₃ of total money = 390 ÷ 2 = 195
³₃ of total money = 3 x 195 = 585

Amount that Gem had at first = $585

Answer(s): $585