# Carlos is 8 years older than Maria. 4 years ago maria was two thirds as old as Carols. How old are they?

Jul 7, 2016

Maria is $28$ and Carlos is $36$.

#### Explanation:

I call the age of Carlos today $C$ and the one of Maria $M$.

The first relationship is

$C = 8 + M$

the second relationship is that

$M - 4 = \frac{2}{3} C$.

I substitute the first in the second

$M - 4 = \frac{2}{3} \cdot \left(8 + M\right)$

$M - 4 = \frac{16}{3} + \frac{2}{3} M$

multiplying by 3 both sides

$3 M - 12 = 16 + 2 M$

$M = 16 + 12$

$M = 28$

and $C$ is

$C = 8 + 28 = 36$.

Just to verify, Carlos is 8 years older of Maria (he is 36 and Maria is 28) and four years ago Maria was 24 that is two third of the age of Carlos.