Question

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?

Answer 1

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=6y`

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

`(x+6)=4(y+6)-3`

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

`6y + 6 = 4y+21 =>y=7,5`

Back substituting we get `x=45`