a) $29
b) $112.50

Let x = initial amount of money.

After buying the watch, Jennifer has (2/3)x.
After mother, Jennifer has (2/3)x + 12.
After buying the dress, Jennifer has (2/3)( (2/3)x + 12) = (4/9)x+8
Thus, (4/9)x+8 = 58, so x = 112.5

Going back to the beginning, with $112.50 as the initial amount. After the watch, Jennifer has $75. Mom gives her $12, so she has $87. The dress is (1/3) this amount, or $29.