Question

A soccer team had a fundraiser where they sold each ticket for a fixed price. After selling 200 tickets, they had a net profit of $12,00. They had to sell a few tickets just to cover necessary production costs of $1,200. Let y represent the net profit (in dollars) when they have sold x tickets. Write an equation for the relationship between the net profit and number of tickets sold.

Answer 1

The linear equation representing the relationship between the net profit (y) and the number of tickets sold (x) for the soccer team's fundraiser is y = 12x - 1,200, indicating the net profit increases by $12 for each additional ticket sold after covering the fixed production costs.

Step-by-step explanation:

Given that a soccer team had to sell a number of tickets to cover their production costs of $1,200 and made a net profit of $1,200 after selling 200 tickets, we can establish a linear equation to represent the relationship between the net profit (y) and the number of tickets sold (x). We know that the profit made after selling a certain number of tickets is the total revenue from ticket sales minus the fixed production costs. To find the fixed price per ticket, we can use the given information that 200 tickets sold resulted in a $1,200 profit, which includes covering the initial $1,200 production costs; therefore, the total revenue for 200 tickets is $1,200 (profit) + $1,200 (costs) = $2,400. Dividing the total revenue by the number of tickets gives us the price per ticket: $2,400 / 200 tickets = $12 per ticket.

The equation representing the net profit based on the number of tickets sold is:

y = 12x - 1,200

This equation illustrates that for every additional ticket sold, the net profit increases by the price of one ticket ($12), after subtracting the initial production costs of $1,200.