# Martina is currently 14 years older than her cousin Joey. In 5 years she will be 3 times as old as Joey. What are their ages?

##### 1 Answer
Nov 13, 2016

Joey is 2 years old now and Martina is 16 years old now.

#### Explanation:

You are comparing the ages of two people and at two different periods of time - the present and in 5 years time.

Let the present age of the younger cousin (Joey) be $x$ years.

Martina is 14 years older now. Her age is $\left(x + 14\right)$ years

In 5 years time , they will both be 5 years older than they are now:

Joey will be $x + 5 \text{ and }$Martina will be $\left(x + 14\right) + 5 = x + 19$

Joey's age, times 3, will be equal to Martina's age....

$3 \times \left(x + 5\right) = x + 19 \text{ } \leftarrow$ solve the equation

$3 x + 15 = x + 19$

$2 x = 19 - 15$

$2 x = 4$

$x = 2 \text{ } \leftarrow$ Joey is 2 years old now

Check: Joey is 2 and Martina is 2+14 = 16

In 5 years time: Joey will be 7 and Martina will be 21.

$3 \times 7 = 21$