Greg and Martin's age when added together come to a total of 60 years. Now Greg is twice as old as Martin was when Greg was half as old as Martin will be when Martin is five times as old as Greg was when Greg was five times as old as Martin. With all this excellent data how old is Greg?

Let G be the age of Greg Let M be the age of Martin

Greg and Martin's age when added together added together come to a total of 60 years.

So,
G+ M = 60
Greg is twice as old as Martin
G = 2M
G+ M = 60
2M + M = 60
3M = 60
M = 20
G = 2 * 20 = 40
Greg was 40 years old

To solve this problem, let's break it down into steps and use variables to represent Greg and Martin's ages.

Step 1: Set up the equations
Let's assign variables to Greg and Martin's ages:
- Let's say Greg's current age is G years.
- Let's say Martin's current age is M years.

Step 2: Translate the given information into equations
From the given information, we can deduce the following equations:
1. "Greg and Martin's age when added together come to a total of 60 years":
G + M = 60

2. "Greg is twice as old as Martin was when Greg was half as old as Martin will be when Martin is five times as old as Greg was when Greg was five times as old as Martin":
G = 2 * (M - (G - 5 * (G - 5 * M))) / 2

Step 3: Solve the equations
Let's solve the equations to find the values of G and M.

Using the first equation:
G + M = 60

Rearranging the equation, we get:
G = 60 - M

Substituting the value of G in the second equation:
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M))) / 2

Simplifying the equation step-by-step:
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M))) / 2
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M)))
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M)))
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M)))
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M)))
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M)))
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M)))

After simplification, we get:
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M)))
60 - M = 2 * (M - (60 - M - 5 * (60 - M - 5 * M)))

Solving this equation will give us the value of M, Martin's current age.

Step 4: Determine Greg's age
Now that we have determined the value of M, we can substitute it back into the first equation to find Greg's age.
G = 60 - M

By solving these equations, we can find the ages of Greg and Martin.