# age-based word problem

Peter's age is three years more than three times his son's age. After three years, Peter's age will be ten years more than twice his son's age. What is Peter's present age?

I have tried to put this into algebra, but not sure if correct?

$x =$ Peter's son's age

$p =$ Peter's age

\begin{align*} 3x + 3 & = p\\ 10 + 2x & = 3 \end{align*}

The first equation ($3x + 3 = p$) is correct, but you lost your focus on the second equation. So now Peter's age is $p$ and his sons age is $x$. After three years, Peter's age will be $p+3$ and his son's $x+3$. So "After three years, Peter's age ($p+3$) will be ten years more than twice his son's age" becomes $$(p+3) = 10 + 2(x+3)$$ When reading this kind of word problems, you just need to keep your head cool, advance slowly and write down exactly what you know.
In fact $x$ and $p$ denote Peter's son's and Peter's age at this moment in time respectively:
$x=$ Peter's son's age right now,
$p=$ Peter's age right now.
So when we talk about peter's son's or his age in three years from now, we are talking about $x+3$ and $p+3$. Therefore we have these equations:
$$\left\{\begin{array}{}p=3x+3\\p+3=10+2(x+3)\end{array}\right.$$