**Mike's age solution**

Let M represent Mike's current age in years and E represent Ed's current age in years.

Let the positive constants a, b and c represent intervals of time in years.

The numerals in column 1 are
used to refer to their respective equations. ** **When equations are merged these numerals will also be merged to identify the resulting equation.

The word "when" identifies
a point in time referenced from the current point in time. ** **Since Mike's current age is M then we know that Mike's age 'a' years ago is simply M-a.

Step 1. ** **Derive the formulas.

The following formulas can be derived by inspection of the statement of the problem.

Be aware of how the word "when" connects points in time.

1 M + E = 44 The sum of Mike's and Ed's ages is 44 years.

2 M = 2 (E – a) Mike is twice as old as Ed was ('a' years ago) when

3 (M – a) = 1/2 (E + b) Mike was half as old as Ed will be ('b' years from now) when

4 (E + b) = 3 (M – c) Ed is three times as old as Mike was ('c' years ago) when

5 (M – c) = 3 (E – c) Mike was three times as old as Ed (then, 'c' years ago).

Step 2. ** **Merge all the equations.

Step 3. ** **Solve for the remaining constants.

Step 4. ** **Assemble in tabular form the ages for the various points in time.

Step 5. ** **Use the table to facilitate a final check of the solution.