let

x = the age of Molly at the moment

y = the age of Mom at the moment

Your little sister Molly is one third the age of your mom

x = y/3 multiply both side by 3

3x = y

y = 3x

In 12 years, Molly will be one half the age of your mom.

x + 12 = (1/2)(y + 12)

plug y = 3x into x + 12 = (1/2)(y + 12)

x + 12 = (1/2)(3x + 12)

by solving the equation we find

x = 12 years

click here to see the step by step solution of the equation

Click to see all the steps

Molly is 12 years old now.