1. **Problem:** Gabriel's age 13 years ago was one-third of his age 7 years hence. Find Gabriel's current age. 2. **Step 1: Define variables.** Let Gabriel's current age be $x$ years. 3. **Step 2: Translate the problem into an equation.** - Gabriel's age 13 years ago: $x - 13$ - Gabriel's age 7 years hence: $x + 7$ - Given: $x - 13 = \frac{1}{3}(x + 7)$ 4. **Step 3: Solve the equation.** $$x - 13 = \frac{1}{3}(x + 7)$$ Multiply both sides by 3 to eliminate the fraction: $$3(x - 13) = x + 7$$ $$3x - 39 = x + 7$$ Subtract $x$ from both sides: $$3x - \cancel{x} - 39 = \cancel{x} + 7$$ $$2x - 39 = 7$$ Add 39 to both sides: $$2x - \cancel{39} + 39 = 7 + 39$$ $$2x = 46$$ Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{46}{\cancel{2}}$$ $$x = 23$$ 5. **Step 4: Conclusion.** Gabriel is currently 23 years old.