To solve for the number of rows of peppers Kendra will plant this year while maintaining the same ratio, we start by identifying the original ratio of tomato rows to pepper rows.
Last year, Kendra planted:
- 6 rows of tomatoes
- 8 rows of peppers
The ratio of tomatoes to peppers is given by: \[ \frac{\text{rows of tomatoes}}{\text{rows of peppers}} = \frac{6}{8} \]
This ratio can be simplified: \[ \frac{6}{8} = \frac{3}{4} \]
This means for every 3 rows of tomatoes Kendra plants, she should plant 4 rows of peppers to keep the same ratio of \( \frac{3}{4} \).
This year, Kendra plans to plant 3 rows of tomatoes. We need to find out how many rows of peppers she will plant, denoted as \( p \). Setting up the ratio equation: \[ \frac{3}{p} = \frac{3}{4} \]
To find \( p \), we can cross-multiply: \[ 3 \times 4 = 3 \times p \] This simplifies to: \[ 12 = 3p \]
Next, we solve for \( p \) by dividing both sides by 3: \[ p = \frac{12}{3} = 4 \]
Thus, Kendra will plant 4 rows of peppers this year.