Question 132308
A girl is now one-fourth as old as her father, and in seven years she will be one-half as old as her father was twelve years ago. Find their present ages.

girl's present age = 1/4 times x = x/4

father's present age = x

girl's age 7 years from now = x/4 + 7

The statement "...one-half as old as her father was twelve years ago" is written 1/2(x - 12).

We now have this equation:

x/4 + 7 = 1/2(x -12)

Before solving for x, we need to remove the fractions.  To do so, multiply both sides of the equation by the LCD, which in this case happens to be 4.

x/4 times 4 = x

7 times 4 = 28

On the left side, we apply the distributive rule to remove the parentheses.

1/2(x - 12) becomes x/2 - 6

Continue to multiply by the LCD 4.

x/2 times 4 = 2x

-6 times 4 = -24

We now have a linear equation and it is:

x + 28 = 2x - 24

Solve for x.

x - 2x = -28 - 24

-x = -52

x = -52/-1

x = 52

Father's age now = 52 years old.

girl's age now = x/4, right?

Replace x with 52 and divide by 4.

52/4 = 13

girl's age now is 13 and her father is 52.

Is this clear?