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.
List their ages at the two different times
NOW:
Mike's age --- x
father's age -- 2x
7 YEARS AGO:
Mike ---- x-7
father ---- 2x-7
It said: " (7 yrs ago) the father was 7 years less than thrice as old as Mike was
---> 2x-7 = 3(x-7) - 7
2x - 7 = 3x - 21 - 7
-x = -21
x = 21
Mike is now 21 , his father now is 42
check:
7 years ago, Mile was 14, his father was35
Is 35 equal to 3 times 14 less 7 ?? YES
To find Mike's present age, we can set up an equation based on the given information.
Let's assume Mike's present age is "M" and his father's present age is "F".
According to the problem, Mike's father is twice as old as Mike, so we can write the equation: F = 2M.
Seven years ago, Mike's age was M - 7, and his father's age was F - 7.
The problem also states that seven years ago, Mike's father was 7 years less than thrice as old as Mike was. So, we can write the equation: F - 7 = 3(M - 7) - 7.
Now we have two equations:
1) F = 2M
2) F - 7 = 3(M - 7) - 7
We can solve these equations simultaneously to find the values of M and F.
From equation 1), we can substitute F = 2M into equation 2):
2M - 7 = 3(M - 7) - 7
Simplifying the equation:
2M - 7 = 3M - 21 - 7
2M - 7 = 3M - 28
Rearranging the equation:
2M - 3M = -21 + 7 - 28
-M = -42
Dividing both sides by -1 to solve for M:
M = -42 / -1
M = 42
Therefore, Mike's present age is 42 years.