Question

Sam is 3 times older than her brother, Owen. In 5 years, Sam will be twice as old as Owen. How old are they now?

Answer 1

Sam is 15; Owen is 5.

Explanation:

Let s denote Sam's age and let o denote Owen's age.

So, Sam is three times older than Owen. Thus:

`s=3o`

In 5 years, Sam will be twice as old as Owen. In other words, Sam's current age plus 5 years will be Owen's current age plus five years times 2. Thus:

`s+5=2(o+5)`

We have a system of equations. Solve for substituting the first equation into the second. Thus:

`3o+5=2(o+5)`

Distribute the right:

`3o+5=2o+10`

Subtract 2o from both sides:

`o+5=10`

Subtract 5 from both sides:

`o=5`

So, Owen is currently 5 years old.

Sam is 3 times older than Owen, so Sam is 15 years old.

And we're done :)