Answer the following questions First Choose the correct answer: 1) If \( 16, x, 2 \) and \( y \) are proportional quantities, then \( \frac{x}{y}=\ldots \) \( \begin{array}{llll}\text { a) } \frac{1}{8} & \text { b) } 32 & \text { c) } \frac{1}{32} & \text { d) } 8\end{array} \)

To find the correct answer, we can set up the proportionality since \( 16, x, 2, y \) are proportional quantities. This gives us the relation: \[ \frac{16}{x} = \frac{2}{y} \] Cross-multiplying, we get: \[ 16y = 2x \] From this, we can express \( \frac{x}{y} \): \[ \frac{x}{y} = \frac{16}{2} = 8 \] So, the correct answer is **d) 8**. Now, let’s dive deeper! In the world of proportional quantities, understanding ratios helps to clarify relationships between different variables. It's like balancing a seesaw; if one side goes up, the other must go down to maintain balance. In this case, knowing that the ratio of \( 16 \) to \( 2 \) dictates how \( x \) and \( y \) relate is a powerful tool in mathematics! When it comes to applying these concepts in real-life situations, consider recipes! When you want to adjust a recipe for more servings, maintaining the ratios of ingredients is key. If you double the amount of flour, you also need to double the sugar to keep things balanced—a perfect real-world application of proportionality at work!