A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs. They sold each ticket for $45. Let y represent the net profit (in dollars) when they have sold x tickets. Which of the following information about the graph of the relationship is given?
Q. A charity organization had to sell 18 tickets to their fundraiser just to cover necessary production costs. They sold each ticket for $45. Let y represent the net profit (in dollars) when they have sold x tickets. Which of the following information about the graph of the relationship is given?
Establish Equation: To determine the relationship between the number of tickets sold x and the net profit y, we need to establish an equation that represents this relationship. We know that the charity organization needs to sell 18 tickets at $45 each to cover their production costs. This means that the break-even point is at 18 tickets.
Calculate Revenue: The total revenue from selling x tickets is given by the equation Revenue=45x, since each ticket is sold for $45.
Determine Cost: The fixed production cost is the cost that the charity needs to cover by selling 18 tickets. This cost is given by Cost=18×45.
Calculate Net Profit: To calculate the net profit y, we subtract the fixed production cost from the total revenue. The net profit equation is y=45x−(18×45).
Simplify Equation: Simplifying the net profit equation, we get y=45x−810.
Graph Relationship: The graph of this relationship would be a straight line with a slope of 45 and a y-intercept of −810. The slope of 45 indicates that for each additional ticket sold, the net profit increases by $45. The y-intercept of −810 indicates that if no tickets were sold, the organization would be at a loss of $810, which corresponds to the production costs.
More problems from One-step inequalities: word problems