6. Ariel has 9 blue beads and 36 purple beads. Ariel has \( n \) times as many purple beads as blue beads. Write and solve an equation to find the value of \( n \).

To find the value of \( n \), we can set up the equation based on the information given. Ariel has 9 blue beads and 36 purple beads, so we can express this as: \[ n = \frac{\text{Number of purple beads}}{\text{Number of blue beads}} = \frac{36}{9} \] Now, solving for \( n \): \[ n = 4 \] Thus, Ariel has 4 times as many purple beads as blue beads. In the realm of ratios and proportions, this problem highlights the beauty of mathematics in understanding relationships. By breaking down the given numbers, you can create simple equations that lead to meaningful interpretations in various real-life scenarios. Whether you're decorating with beads or analyzing data, these principles can help you find balance and make informed decisions!