# Linear Equation In One Variable

• Feb 15th 2011, 08:02 AM
rn5a
Linear Equation In One Variable
The sum of the present ages of father & son is 99 years. When the father was as old as his son is now, his age was four times the age of his son at that time. How do I find the present age of father & son?

Thanks,

Ron
• Feb 15th 2011, 10:58 AM
rome
Son is 19.8 years old; father is 79.2 years old.

Call the age of the father F, and the son's age S.

You know the combined age of the father and son:

$F + S = 99$ (equation 1)

And you know that the father is four times older than the son:

$F = 4S$ (equation 2)

So you've just got simultaneous equations.

Rearrange and substitute and you arrive at two more equations, one of which tells you the age of the father, and the other tells you the age of the son:

$S = 99 / 5$

...and...

$F = 396 / 5$
• Feb 15th 2011, 11:50 AM
earboth
Quote:

Originally Posted by rn5a
The sum of the present ages of father & son is 99 years. When the father was as old as his son is now, his age was four times the age of his son at that time. How do I find the present age of father & son?

Thanks,

Ron

1. Age of father today: x
Age of son today: 99 - x

2. Time difference between the two ages: x - (99 - x) = 2x - 99

3. When the father was 2x-99 years younger he had the age of his son today:
99 - x
Age of the son in the past: 99 - x - (2x-99) = 198 - 3x

4. This age of the son was a quarter of the age of his father:

$\boxed{99 - x = 4(198 - 3x)}$

5. Solve for x.