Q \( \begin{array}{c}y \text { varies directly with } x \text {. } \\ y \text { is } 44 \text { when } x \text { is } 11 \text {. } \\ \text { What is } y \text { when } x \text { is } 8 \text { ? } \\ y=[?]\end{array} \)

To solve this problem, we start by determining the constant of proportionality, \( k \), since \( y \) varies directly with \( x \). We know that when \( x = 11 \), \( y = 44 \). Thus, we can express this relationship as \( y = kx \), so \( 44 = k \cdot 11 \). Solving for \( k \), we find \( k = \frac{44}{11} = 4 \). Now, we want to know what \( y \) is when \( x = 8 \). Using the relationship, we plug in our known value of \( k \): \[ y = 4 \cdot 8 = 32. \] So when \( x = 8 \), \( y \) is \( 32 \). Answer: \( y = 32 \) For a related twist, let’s say you’re in a grocery store and see that you can buy 11 oranges for $44. This lets you calculate that each orange costs $4! Now, if you want just 8 oranges, hey, you can quick-math that it would cost you just $32! Fun, right? Proportionality isn’t just for math class; you can use it in everyday shopping! Did you know throughout history, ideas of direct variation have appeared in business as well? In ancient trade, merchants often used ratios to set prices based on quantities. Whether it was gold, spices, or textiles, understanding the relationship between quantity and price was vital. So the next time you're calculating a recipe or shopping, remember, you’re standing on the shoulders of traders from long ago!