W) Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. 4) A baseball coach takes his team out for pizza every time they win a game. Not everyone can come each time, so he orders the pizzas based on how many players are coming. After last week's victory, he bought 1 small pizza and 2 large pizzas, the perfect amount for the 15 players going out for pizza. This week, there were 33 players going, so he ordered 3 small pizzas and 4 large pizzas, which was also just the right amount. How many people does each size of pizza feed? Sach sfnall pizza feeds Save answer

Let \( x \) represent the number of players fed by a small pizza and \( y \) represent the number fed by a large pizza. From the information given, we can set up the following system of equations based on player counts: 1. \( x + 2y = 15 \) (1 small pizza and 2 large pizzas feed 15 players) 2. \( 3x + 4y = 33 \) (3 small pizzas and 4 large pizzas feed 33 players) Now let's solve this system of equations. From the first equation, we can express \( x \) in terms of \( y \): \[ x = 15 - 2y \] Substituting \( x \) into the second equation: \[ 3(15 - 2y) + 4y = 33 \] \[ 45 - 6y + 4y = 33 \] \[ 45 - 2y = 33 \] \[ -2y = 33 - 45 \] \[ -2y = -12 \] \[ y = 6 \] Now substituting back to find \( x \): \[ x = 15 - 2(6) = 15 - 12 = 3 \] Thus, each small pizza feeds **3 players** and each large pizza feeds **6 players**. --- Ever wonder how pizza rules relate to history? The concept of communal eating and sharing food dates back to ancient Rome, where venues called thermopolia served hot meals, much like modern pizza places. They were often bustling social spots! For those keen on diving deeper, check out "Pizza: A Global History" by Carol Helstosky. It delves into how pizza transformed from humble beginnings in Italy to becoming an international favorite, blending cultural influences and tastes. Yum!