1. **Problem statement:** The sum of the present ages of a father and son is 80 years. When the father's age was equal to the present age of the son, their combined ages summed to 40 years. Find their present ages. 2. **Define variables:** Let the present age of the father be $F$ and the present age of the son be $S$. 3. **Given equation 1:** $$F + S = 80$$ 4. **Analyze the second condition:** When the father's age was equal to the present age of the son, let the number of years ago be $x$. Then: - Father's age at that time: $F - x$ - Son's age at that time: $S - x$ Since the father's age at that time equals the present age of the son: $$F - x = S$$ 5. **Sum of their ages at that time:** $$ (F - x) + (S - x) = 40 $$ Simplify: $$ F + S - 2x = 40 $$ 6. **Substitute $F + S = 80$ from step 3:** $$ 80 - 2x = 40 $$ $$ 2x = 80 - 40 = 40 $$ $$ x = 20 $$ 7. **Use $F - x = S$ to find $F$ and $S$:** $$ F - 20 = S $$ 8. **Substitute $S$ in $F + S = 80$:** $$ F + (F - 20) = 80 $$ $$ 2F - 20 = 80 $$ $$ 2F = 100 $$ $$ F = 50 $$ 9. **Find $S$:** $$ S = F - 20 = 50 - 20 = 30 $$ **Final answer:** The present age of the father is 50 years and the present age of the son is 30 years.