1. **State the problem:** We have two types of energy drinks: 2-Liter jugs costing 4 each and 0.5-Liter bottles costing 1.5 each. A trainer buys a total of 15 Liters and pays exactly 35. 2. **Define variables:** Let $x$ = number of 2-Liter jugs Let $y$ = number of 0.5-Liter bottles 3. **Write the linear equations:** A. Total Liters equation: $$2x + 0.5y = 15$$ B. Total Cost equation: $$4x + 1.5y = 35$$ 4. **Solve the system:** From the first equation, multiply both sides by 2 to clear decimals: $$2(2x + 0.5y) = 2(15) \Rightarrow 4x + y = 30$$ Rewrite the system: $$\begin{cases} 4x + y = 30 \\ 4x + 1.5y = 35 \end{cases}$$ Subtract the first equation from the second: $$ (4x + 1.5y) - (4x + y) = 35 - 30 \Rightarrow 0.5y = 5 $$ Solve for $y$: $$ y = \frac{5}{0.5} = 10 $$ Substitute $y=10$ into the first equation: $$ 4x + 10 = 30 \Rightarrow 4x = 20 $$ Divide both sides by 4: $$ x = \frac{20}{4} = 5 $$ 5. **Interpretation:** The trainer bought 5 jugs and 10 bottles. **Final answer:** $$x=5, \quad y=10$$