A mother's age is $19$ years more than the sum of the ages of her sons A mother's age is $19$ years more than the sum of the ages of her two sons. $5$ years ago, the mother's age was $4$ times than the sum of the ages of her two sons. What is the age of the older child?


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*Let's say the sum of the ages of her sons is $x$, the mother's age will be $x+19$. 
$5$ years ago, $x-5$ = $x+19-5$. However, I believe that I've gone too wrong. 

*What kind of methods can I use to solve this question? 
I'll be waiting for your professional helps. 
My Kindest Regards!
 A: There isn't enough information to solve for the age of the older child, even if there are two children. I can only solve for the following:
$\text{Ages of sons combined} = x$
$\text{Mother's age}=y$
$$x+19=y$$
$$4(x-10)=y-5$$
$$4x-40=x+19-5$$
$$3x=54$$
$$x=\dfrac {54}{3}=18$$
You know the sums of the ages of the two sons is $18$. But, you need to find the age of one of the children to find the age of the other child.
Note that the younger child must be older than $5$ years but younger than $9$ years. For example, if the younger child is $7$ years old, then the older child is $11$ years old.
A: $$\begin{align}
M &= \text{mother’s current age in years} \\
S &= \text{older son’s current age in years} \\
s &= \text{younger son’s current age in years}
\end{align}$$
The first statement translates to
$$M = 19+S+s$$
The second statement translates to
$$M-5 = 4\bigl( (S-5)+(s-5) \bigr)$$
We also know logically that any solutions, if they exist, should be restricted to
$$\begin{align}
M &> S >0 \\
S &> s >0\\
M &> s >0
\end{align}$$
Can you take things from there? How does the number of variables compare to the number of equations?
A: hint
Today
$$y=x+19$$
five years ago
$$y-5=4 (x-5n) $$
$$14=3x-20n$$
$n $ is the number of sons.
The sum $x $ must satisfy $x>5n $
thus $n=2$ and
$x=18$ years .
the mother has
$37$ years .
