Math linear algebra age problems

Question

Travis is 66 years younger than Alicia 7 years ago Alicia's age was 3 times Travis age how old is Travis now? What's the formula

Answer 1

There's no particular formula for this. But you can do it this way -

Let Alicia' age be $x$ and Travis' age be $y$.

So, $y$ = $x - 66 \implies x = y+66$ .....(1)
Also, $x-7 = 3(y-7)$
$\implies x-7 = 3y-21$
$\implies x=3y-14$ .....(2)

So, from (1) and (2);
$y+66 = 3y-14$

$\implies y=40$

Answer 2

Well, another way to solve it is to let $T$ and $A$ be the ages of Travis and Alicia 7 years ago respectively. Therefore, you must solve: $$\begin{cases} T+66=A \\ A=3T \end{cases}$$ After solving this system, just add $T$ by $7$ to get Travis' current age.