Question

a charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. after selling 10 tickets, they were still at a net loss of $800 (due to the production costs). they sold each ticket for $70. let y represent the net profit (in dollars) when they have sold x tickets. complete the equation for the relationship between the net profit and number of tickets sold. y =

Explanation:

Step1: Determine the revenue from selling x tickets

The revenue from selling \( x \) tickets at $70 per ticket is \( 70x \) dollars.

Step2: Find the fixed cost (production cost)

After selling 10 tickets, revenue is \( 70\times10 = 700 \) dollars, and net loss is $800. Let \( C \) be the production cost. We know that \( \text{Profit} = \text{Revenue} - \text{Cost} \), so when \( x = 10 \), \( y=-800 \). Substituting into the profit formula: \( -800=70\times10 - C \). Solving for \( C \): \( C = 700 + 800=1500 \) dollars.

Step3: Form the profit equation

The net profit \( y \) is revenue minus cost. So \( y = 70x - 1500 \).

Answer:

\( 70x - 1500 \)