Esther spent some of her money on a sweater, a pair of canvas shoes and some rings. She spent ¹₅ of her money and an additional $143 on a sweater. Next, she spent ⁵₇ of the remaining money and an additional $42 on a pair of canvas shoes. Finally, she spent ³₄ of what she had left on some rings and had $13 left. How much did Esther 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 $42 spent on a pair of canvas shoes
= 1 - ⁵₇
= ²₇

²₇ of the remaining money = 52 + 42 = 94
¹₇ of the remaining money = 94 ÷ 2 = 47
⁷₇ of the remaining money = 7 x 47 = 329

Fraction of the total money excluding the additional $143 spent on the sweater
= 1 - ¹₅
= ⁴₅

⁴₅ of total money = 329 + 143 = 472
¹₅ of total money = 472 ÷ 4 = 118
⁵₅ of total money = 5 x 118 = 590

Amount that Esther had at first = $590

Answer(s): $590