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#