Brandon's recipe for lemon water consists of 1 cup of sliced lemon for every 2 cups of water. To determine how many cups of sliced lemon he would need for 12 cups of water, we can set up a proportion based on the ratio of sliced lemon to water.
Given:
- 1 cup of sliced lemon corresponds to 2 cups of water.
We need to find out how many cups of sliced lemon (let's call it \( x \)) he needs for 12 cups of water. We can set up the equation:
\[ \frac{1 \text{ cup of lemon}}{2 \text{ cups of water}} = \frac{x \text{ cups of lemon}}{12 \text{ cups of water}} \]
Cross-multiplying gives:
\[ 1 \cdot 12 = 2 \cdot x \]
This simplifies to:
\[ 12 = 2x \]
To solve for \( x \), divide both sides by 2:
\[ x = \frac{12}{2} = 6 \]
Thus, Brandon would need to add 6 cups of sliced lemon to 12 cups of water.