1. **State the problem:** 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, the sum of their ages was 40 years. We need to 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. **Write the first equation:** The sum of their present ages is 80. $$F + S = 80$$ 4. **Analyze the second condition:** When the father's age was equal to the present age of the son, the sum of their ages was 40. Let the number of years ago when this happened be $x$. Then: - Father's age at that time: $F - x$ - Son's age at that time: $S - x$ Given that at that time, father's age was equal to the present age of the son: $$F - x = S$$ Also, the sum of their ages at that time was 40: $$(F - x) + (S - x) = 40$$ 5. **Use the equation $F - x = S$ to express $x$:** $$x = F - S$$ 6. **Substitute $x$ into the sum equation:** $$ (F - (F - S)) + (S - (F - S)) = 40 $$ Simplify: $$ S + (S - F + S) = 40 $$ $$ S + 2S - F = 40 $$ $$ 3S - F = 40 $$ 7. **Use the first equation $F + S = 80$ to express $F$:** $$ F = 80 - S $$ 8. **Substitute $F$ into $3S - F = 40$:** $$ 3S - (80 - S) = 40 $$ $$ 3S - 80 + S = 40 $$ $$ 4S - 80 = 40 $$ $$ 4S = 120 $$ $$ S = 30 $$ 9. **Find $F$ using $F = 80 - S$:** $$ F = 80 - 30 = 50 $$ **Final answer:** The present age of the father is 50 years and the present age of the son is 30 years.