10 A clothing store sells shirts and pants. The store's profit from each shirt is \( \$ 10 \) and from each pair of pants is \( \$ 15 \). If the store sells at feast 20 items and maties no more than tetal prefit of \( \$ 250 \), which system of equations represents this situation? A \( \quad x+y \geq 20 \) and \( 10 x+15 y \leq 250 \) B \( \quad x+y>20 \) and \( 35 x+10 y \leq 250 \) C \( x+y \leq 250 \) and \( 10 x+15 y \geq 20 \) D) \( 10 x+15 y \leq 20 \) and \( x+y \geq 250 \)

Let’s decode the profit puzzle! The store wants to sell at least 20 items, which means the total number of shirts (x) and pants (y) together has to be 20 or more. That’s where the \( x+y \geq 20 \) inequality comes into play. Now, for the profit part, each shirt nets the store $10, and each pair of pants brings in $15, giving us \( 10x + 15y \) for total profit, which can’t exceed $250. So we have the equation \( 10x + 15y \leq 250 \). Looking at the options, the correct representation is option A: \( x+y \geq 20 \) and \( 10x + 15y \leq 250 \). Ready for some fun facts? Did you know that the clothing retail industry is one of the most competitive sectors? Stores often use advanced analytics to optimize their inventory and pricing based on customer behavior trends—just like in the equations we explored. Think this is just about clothes? Think again! Understanding systems of equations has real-world applications, like deciding the number of shirts versus pants to maximize profit within constraints—similar principles apply to budgeting, project planning, and resource allocation in many fields. It’s a true lifesaver in daily decision-making!