Final answer:
To find the son's birth year, we used the given condition of the father-son age relationship in 2052 B.S. and 2080 B.S., set up an equation, and solved for the son's age. The calculations revealed that the son was born in 1968 B.S.
Step-by-step explanation:
The question requires us to determine the son's birth year based on the age relationship between the father and son in two different years. We're given that the father was 3 times as old as his son in 2052 B.S. and 5/2 times as old in 2080 B.S.
Let's denote the son's age in 2052 B.S as 's' and the father's age at that time as '3s'. By 2080 B.S., the son would be 's + 28' years old and the father would be '3s + 28' years old. According to the second condition, the father is 5/2 times as old as the son in 2080 B.S., so we set up the equation 3s + 28 = (5/2) * (s + 28).
Solving the equation, we get:
- 3s + 28 = (5/2)(s + 28)
- 6s + 56 = 5s + 140 (Multiplying both sides by 2 to clear the fraction)
- s = 140 - 56 (Subtracting 5s and 56 from both sides)
- s = 84 (Calculating the difference)
So, the son was 84 years old in 2052 B.S. Since we are looking for the son's birth year, we subtract 84 from 2052 B.S to determine the son's birth year: 2052 - 84 = 1968 B.S.
The son was therefore born in 1968 B.S.