Tom is 6 times as old as Todd. In 6 years Tom's age will be 3 years less than 4 times as old as Todd. How old is Tom?

Sep 29, 2015

Tom is 45 and Todd is 7,5.

Explanation:

Let Tom's age now be $x$ and let Todd's age now be $y$.

Now write the information given as equations in terms of x and y.

Since Tom is 6 times as old as Todd, it implies that

$x = 6 y$

In 6 years time, Tom will be $x + 6$ and Todd will be $y + 6$.
But Tom will be 3 years less than 4 times Todd at that time so the equation becomes

$\left(x + 6\right) = 4 \left(y + 6\right) - 3$

Now substituting x with 6y and solving for y we get

$6 y + 6 = 4 y + 21 \implies y = 7 , 5$

Back substituting we get $x = 45$