Jesmin spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourth of what she had left on food. She had 500 left over. How much money did she start with?

Let us consider that she had x at the beginning.

She spent on books= x/3

Remainder after books purchase= (x - x/3)

She spent on clothing= (x - x/3) / 2

Remainder after cloth purchase = (x - x/3) / 2

She spent on food= 3[(x - x/3) / 2] / 4 = 3[(x - x/3) / 8] = (3x - x) / 8

                                                                             = 2x / 8