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?

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Answer 1 · 2015-09-29T11:05:05

Tom is 45 and Todd is 7,5.

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 $x=45$