3. A company produces a lemon drink by diluting lemon juice with water. Initially, the company produced a drink containing $15\%$ lemon juice. After some time, the CEO ordered to reduce the lemon juice content to $10\%$. By what percentage will the amount of lemon drink produced increase with the same volumes of lemon supplies?
Answer: By $50 \%$.

Solution. Method 1. The content of lemon juice in the drink after the CEO's directive decreased by one and a half times. This means that from the same lemons, one and a half times more lemon drink can be made. In other words, the amount of lemon drink produced will increase by one and a half times or by $50 \%$.

$\underline{2}$ Method. Let $x$ be the amount of drink produced before the CEO's directive. Then the amount of lemon juice in this drink is $-0.15 \cdot x$. Let $y$ be the amount of drink produced after the CEO's directive. Then the amount of lemon juice in this drink is $-0.1 \cdot y$. Since it is assumed that the amount of lemon juice has not changed, we get the equation $0.15 \cdot x = 0.1 \cdot y$. Multiplying both sides of this equation by 10, we get: $y = 1.5 \cdot x$; or: $y = x + 0.5 \cdot x$. Therefore, the amount of drink produced has increased by $50 \%$.

## Grading Criteria.

- Full solution - 7 points.
- The equation is correctly set up according to the problem statement, but further reasoning is missing or incorrect - 2 points.
- The correct answer is obtained using a specific amount (for example, 100 liters) of the produced drink or lemon juice - 1 point.
- Only the correct answer is provided or the correct answer is accompanied by incorrect reasoning - 0 points.