Question 102516
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
{{{m = 4d}}}
We also know in 3 years Tom's age will be 13 years more than 2 times as old as Todd, so
{{{m + 3 = 2(d+3) + 13}}}
Now we can plug the first equation into the second to get:
{{{4d + 3 = 2(d+3) + 13}}}
Use the distributive property on the right side of the equation.
{{{4d + 3 = 2d+6 + 13}}}
Combine like terms
{{{4d + 3 =  2d + 19}}}
Subtract 2d from each side
{{{2d + 3 = 19}}}
Subtract 3 from each side
{{{2d = 16}}}
Divide each side by 2
{{{d = 8}}}
So we now know Todd is 8. We can plug that in to find Tom's age.
{{{m = 4 * 8}}}
{{{m = 32}}}
Tom is 32.
We can check this by using the second equation.
{{{m + 3 = 2(d+3) + 13}}}
{{{32 + 3 = 2(8+3) + 13}}}
{{{35 = 2 * 11 + 13}}}
{{{35 = 22 + 13}}}
{{{35 = 35}}}
Check.
That's all for this problem.
-Mike