# Question #eae6b

Feb 3, 2017

Peter is 13 and Luke is 24.

#### Explanation:

Suppose Luke is $L$ years old and Peter is $P$ years old.

Here is how you write "Luke's age is 2 less than twice Peter's age":
$L = 2 P - 2$

Here is how your write "The sum of their ages is 37":
$L + P = 37$

We can replace $L$ with $2 P - 2$ in the second equation.

$\textcolor{red}{L} \text{ } + P = 37$
$\textcolor{red}{2 P - 2} + P = 37$
$3 P - 2 = 37$
$3 P = 39$
$P = 13$. So Peter is 13 years old.

Now you can replace $P$ with $13$

$L = 2 \cdot \textcolor{red}{P} - 2$
$L = 2 \cdot \textcolor{red}{13} - 2$
$L = 26 - 2$
$L = 24$. So Luke is 24 years old.