SOLUTION: 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.

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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.
Found 2 solutions by checkley71, nycsharkman:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
LET THE GIRL'S AGE = X & HER FATHER'S AGE = 4X WHICH IS THERE AGES NOW.
IN 7 YEARS THE GIRL'S AGE WILL BE (X+7).
IN 7 YEARS THE FATHER'S AGE WILL BE(4X+7).
(X+7)=(4X-12)/2
X+7=(4X-12)/2 NOW CROSS MULTIPLY
2(X+7=4X-12
2X+14=4X-12
2X-4X=-12-14
-2X=-26
X=-26/-2
X=13 YEARS OLD FOR THE GIRL NOW.
4*13=52N AGE OF THE DAD NOW.
PROOF
13+7=(4*13-12)/2
20=(52-12)/2
20=40/2
20=20

Answer by nycsharkman(136) (Show Source):
You can put this solution on YOUR website!
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?