If the father is f and the son is s, then we know
f-7 = 7(s-7)
f+3 = 3(s+3)
Now just solve for f and s
f-7 = 7(s-7)
f+3 = 3(s+3)
Now just solve for f and s
Let's say the current age of the son is S years.
Therefore, the current age of the man is M years.
According to the given information:
"The age of a man 7 years ago was seven times the age of his son."
This can be expressed as:
M - 7 = 7(S - 7)
Simplifying this equation, we have:
M - 7 = 7S - 49
Next, let's consider the second part of the information:
"Father's age after 3 years will be three times the age of the son."
This can be expressed as:
M + 3 = 3(S + 3)
Simplifying this equation, we have:
M + 3 = 3S + 9
Now we have a system of two equations:
1) M - 7 = 7S - 49
2) M + 3 = 3S + 9
To solve this system of equations, we can use the substitution or elimination method.
Let's use the elimination method:
Multiply the first equation by 3:
3(M - 7) = 3(7S - 49)
3M - 21 = 21S - 147
3M - 21S = -126 ----(equation 3)
Subtract equation 2 from equation 3:
(3M - 21S) - (M + 3) = -126 - 9
2M - 22S = -135 ----(equation 4)
Now we have a new equation (equation 4), which is:
2M - 22S = -135
We can now solve equation 4 to find the values of M (man's age) and S (son's age).
However, it is important to note that the equation has infinitely many solutions and does not have a unique answer. This means that there are multiple sets of values for M and S that satisfy the given conditions.
To find a specific solution, we will need additional information or constraints.