SOLUTION: Tom is 4 times as old as Todd. In 3 years Tom's age will be 13 years more than 2 times as old as Todd. How old is Tom?

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Let m = Tom's age
Let d = Todd's age
Now we have to write equations that compare their ages.
We know tom is 4 times as old as Todd, so

We also know in 3 years Tom's age will be 13 years more than 2 times as old as Todd, so

Now we can plug the first equation into the second to get:

Use the distributive property on the right side of the equation.

Combine like terms

Subtract 2d from each side

Subtract 3 from each side

Divide each side by 2

So we now know Todd is 8. We can plug that in to find Tom's age.


Tom is 32.
We can check this by using the second equation.





Check.
That's all for this problem.
-Mike