What are the nex three numbers in the following sequence? 4, 13/3, 14/3, 5, 16/3.

Ask yourself:  by what number (a fraction) must we multiply 4 to obtain 13/3?  Try (13)/(4*3).

Check:  Does     13
                          * 4 equal 13/3?  Yes.
                          4(3)

Check again.  Does    13            13
                                  *  =  14/3 ?  No
                                    4(3)          3

Try something different.  Convert 4 to 3(4)
                                                             
                                                               3

Then we have 12/3, 13/3, 14/3, 15/3, 16/3 (different numerators, same 
                                                                                       denominator)

Continuing, 17/3, 18/3, 19/3, and so on.

Joe is 9 years old

Step-by-step explanation:

We can start by creating two different equations, one for each fact that we know about their ages.

Say that J is Joe's age

Say that T is Tim's age

Our first equation would then be:

4J + 2T = 50

J - 2 = T

Now that we know that T is J - 2, we can plug that in to the first equation.

4J + 2(J - 2) = 50

We can simplify this equation to solve for J

4J + 2J - 4 = 50

6J = 54

J = 9

Joe is 9 years old