1. **Problem statement:** Fred is 4 years older than Barney. Five years ago, the sum of their ages was 48. Find their current ages. 2. **Define variables:** Let $B$ be Barney's current age and $F$ be Fred's current age. 3. **Translate the problem into equations:** - Fred is 4 years older than Barney: $$F = B + 4$$ - Five years ago, sum of their ages was 48: $$(F - 5) + (B - 5) = 48$$ 4. **Simplify the second equation:** $$F - 5 + B - 5 = 48$$ $$F + B - 10 = 48$$ $$F + B = 58$$ 5. **Substitute $F$ from the first equation into the second:** $$ (B + 4) + B = 58$$ $$2B + 4 = 58$$ 6. **Solve for $B$:** $$2B = 58 - 4$$ $$2B = 54$$ $$B = \frac{\cancel{2}B}{\cancel{2}} = \frac{54}{2} = 27$$ 7. **Find $F$ using $F = B + 4$:** $$F = 27 + 4 = 31$$ 8. **Answer:** Barney is 27 years old and Fred is 31 years old now.