Graphing Rue's Budget: Paninis, Drinks, and Theme Park Tickets

To help Rue plan her purchases, let's create a coordinate system that shows all her possible choices.The horizontal axis shows the number of panini and drink combinations she could buy at twelve dollars each.The vertical axis represents the number of theme park tickets at forty-five dollars each.Every point on this graph represents a different combination of purchases Rue could make.For example, let's look at the point two comma one.This point represents buying two panini-drink combos and one theme park ticket.Notice how we're only using the positive part of the coordinate system.This makes sense because Rue can't buy negative tickets or negative meals!We'll be focusing on whole number points, since Rue can't buy partial tickets or partial meals.These points represent the realistic combinations Rue could choose from.Now that we understand how to read our coordinate system, we can start exploring Rue's budget constraints.Now that we have our coordinate system, let's plot Rue's budget line using the equation: twelve x plus forty-five y equals one hundred eighty.To find our first point, let's set x to zero and solve for y.When we set y to zero, we can solve for x.These two points will define our budget line.The budget line represents all combinations of purchases that cost exactly one hundred eighty dollars.Any point above this line represents combinations that exceed Rue's budget.While points below the line represent affordable combinations.Let's find some additional points along this line to better understand our options.Remember, while these decimal values help us understand the budget line, Rue will need to choose whole number combinations for her actual purchases.Now that we have our budget line, let's analyze specific purchase combinations.First, let's identify all possible whole-number combinations, since Rue can't buy partial tickets or meals.Let's look at our first example. Rue could buy 7 panini-drink combos and 2 theme park tickets.Another option is 3 combos and 3 tickets, which costs one hundred and seventy-one dollars.The maximum number of tickets Rue could buy is 4, spending her entire budget on tickets.Alternatively, she could buy 15 panini-drink combos and no tickets.Here are all the practical integer combinations that stay within Rue's budget.Among these options, getting 3 tickets and 3 combos offers a balanced choice, while 4 tickets maximizes theme park visits.