# Tom is 3 times as old as jerry, in 10 years he will be twice as old as jerry will be then, how old are the boys now?

Aug 3, 2015

Tom is $30$ and Jerry is $10$.

#### Explanation:

You were given two pieces of information, one about the relationship between the current ages of the boys, and the other about the relationship between their ages 10 years from now.

These two pieces of information will become two equations with two variables, Tom's age,$T$, and Jerry's age, $J$.

So, you know that at this point in time, Tom is three times older than Jerry. This means that you can write

$T = 3 \cdot J$

Ten years from now, the two ages of the boys, which have increased by $10$ years, have a different relationship. More specificallly, Tom's age is now only twice Jerry's age.

This means that you can write

${\underbrace{T + 10}}_{\textcolor{b l u e}{\text{Tom's age in 10 years")) = 2 * underbrace((J+10))_(color(blue)("Jerry's age in 10 years}}}$

This will be your system of equations

$\left\{\begin{matrix}T = 3 J \\ T + 10 = 2 \left(J + 10\right)\end{matrix}\right.$

To solve this system, replace $T$ wwith the value you have from the first equation into the second equation and solve for $J$.

$T = 3 J$

$3 J + 10 = 2 J + 20 \implies J = \textcolor{g r e e n}{10}$

This means that $T$ will be

$T = 3 \cdot J$

$T = 3 \cdot 30 = \textcolor{g r e e n}{30}$

The two ages of the boys are

$\left\{\begin{matrix}T = 30 \\ J = 10\end{matrix}\right.$