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.