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. **Write the equations:** Let $x$ be the number of 2-Liter jugs and $y$ be the number of 0.5-Liter bottles. - Total Liters: $$2x + 0.5y = 15$$ - Total Cost: $$4x + 1.5y = 35$$ 3. **Solve the system:** From the first equation, multiply both sides by 2 to clear decimals: $$2(2x + 0.5y) = 2(15) \Rightarrow 4x + y = 30$$ 4. **Rewrite the system:** $$\begin{cases} 4x + y = 30 \\ 4x + 1.5y = 35 \end{cases}$$ 5. **Subtract the first equation from the second:** $$ (4x + 1.5y) - (4x + y) = 35 - 30 $$ $$ 4x - \cancel{4x} + 1.5y - y = 5 $$ $$ 0 + 0.5y = 5 $$ 6. **Solve for $y$:** $$ y = \frac{5}{0.5} = 10 $$ 7. **Substitute $y=10$ into the first equation:** $$ 4x + 10 = 30 $$ $$ 4x = 30 - 10 $$ $$ 4x = 20 $$ 8. **Solve for $x$:** $$ x = \frac{20}{4} = 5 $$ **Answer:** The trainer buys 5 jugs and 10 bottles.