# In eight years, peter will be three times old as he was eight years ago, how old is peter now?

Sep 3, 2015

$16$

#### Explanation:

Writing $p$ for Peter's current age in years, we are given:

$p + 8 = 3 \left(p - 8\right) = 3 p - 24$

Add $24$ to both ends to get:

$p + 32 = 3 p$

Subtract $p$ from both sides to get:

$32 = 2 p$

Divide both sides by $2$ to get:

$p = 16$

Sep 3, 2015

Peter is 16 years old now.

#### Explanation:

Since you're only dealing with Peter's age at various points in time, you will only need to write one equation.

Let's say that Peter's age is $x$ now. You know that eight years from now, Peter will be three times as old as he was eight years ago.

If you take Peter's age eight years from now to be $x + 8$, and his age eight years ago to be $x - 8$, then you have

$x + 8 = 3 \cdot \left(x - 8\right)$

Solve this equation for $x$ to get Peter's current age

$x + 8 = 3 x - 24$

$2 x = 32 \implies x = \frac{32}{2} = \textcolor{g r e e n}{16}$

So, eight years ago Peter was 8. Eight years from now, which is equivalent to 16 years from when he had 8 years, he will be 24.

Sep 3, 2015

Peter is currently $16$ years old

#### Explanation:

Let's represent peter's age by the variable $x$

In eight years Peter will be $\left(x + 8\right)$ years old

Eight years ago Peter was $\left(x - 8\right)$ years old

The problem says that $\left(\text{in eight years")=3xx("eight years ago}\right)$

Mathematically,
$\left(x + 8\right) = 3 \left(x - 8\right)$

Now, we just solve this equation for $x$

$\left(x + 8\right) = 3 \left(x - 8\right)$
$\implies x + 8 = 3 x - 24$
$\implies 3 x - x = 24 + 8$
$\implies 2 x = 32$
$\implies x = 16$

Hence, Peter is currently $\textcolor{b l u e}{16}$ years old.