# Fred is 4 years older than Barney. Five years ago the sum of their ages was 48. How old are they now?

Apr 8, 2018

Fred is $31$ years old

Barney is $27$ years old

#### Explanation:

Let Fred's age be denoted as $F$, and Barney's as $B$.

Then, $F = B + 4$ (in years).

Five years ago, the sum of their ages was $48$:

$R i g h t a r r o w F + B = 48$

$R i g h t a r r o w \left(B + 4\right) + B = 48$

$R i g h t a r r o w 2 B = 44$

$\therefore B = 22$

So, five years ago Barney was $22$ years old.

Let's find out how old Fred was five years ago:

$R i g h t a r r o w F = B + 4 = 22 + 4 = 26$

Fred was $26$ years old, five years ago.

Therefore, Fred is now $26 + 5 = 31$ years old and Barney is $22 + 5 = 27$ years old.