Mathematical approach exercise

Question

I have this statement:

A father have $x$ years old, and his son $y$ years old.

¿Within how many years the age of father will be four times the age of his son?

$x =$ Father years, $y =$ Son years

$x - y =$ Year of the birth of his son.

The father will be 4 times the age of his son, when:

$\frac{x}{4} = y$ or analogously $x = 4y$

But my try was incorrect, because the correct answer was: $\frac{x-4y}{3}$

so, how to get to that answer? and what am I doing wrong?

It is not necessary. It is for me enough you have detected your mistake of reasoning. I like to teach to beginners it is very pleasant for me. Regards. — Piquito, Mar 11 '18 at 19:38

score 0 · Accepted Answer · answered Mar 13 '18 at 07:26

As pointed out the answer is $\frac{x-4y}{3}$

Given the father and son's ages as $x_1$ and $y_1$, respectively, you can ask how many years $X$ will pass for $x_2=4y_2$ where $x_2=x_1+X$ and $y_2=y_1+X$ and thus: $$x_1+X=4(y_1+X)\Rightarrow \bbox[yellow,5px]{X=\frac{x_1-4y_1}{3}}$$

Mathematical approach exercise

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