Mike’s father is twice as old as he is. Seven years ago, the father was 7 years less than thrice as old as Mike was. Find Mike’s present age.
To solve this problem, let's start by assigning variables to the ages of both Mike and his father. Let's assume Mike's age is M years, and his father's age is F years.
According to the given information, "Mike’s father is twice as old as he is," we can write the equation:
F = 2M ......(equation 1)
The second piece of information states that "Seven years ago, the father was 7 years less than thrice as old as Mike was." This can be expressed as:
(F - 7) = 3(M - 7) .......(equation 2)
Now, we have two equations (equation 1 and equation 2) with two variables (M and F), which we can solve to find Mike's present age.
Substituting equation 1 into equation 2, we get:
(2M - 7) = 3(M - 7)
Expanding the equation:
2M - 7 = 3M - 21
Bringing like terms to one side:
2M - 3M = -21 + 7
-M = -14
Dividing both sides by -1, we get:
M = 14
Therefore, Mike's present age is 14 years.