A charity organization had a fundraiser where each ticket was sold for a fixed price. After selling 200 tickets, they had a net profit of $12,000. They had to sell a few tickets just to cover necessary production costs of $1200.

Question

Vocaloid · Answer

full question: A charity organization had a fundraiser where each ticket was sold for a fixed price. After selling 200 tickets, they had a net profit of $12,000. They had to sell a few tickets just to cover necessary production costs of $1200. 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.

Vocaloid · Answer

in general, net profit = revenue - expenses

the total revenue is simply (price per ticket)(# of tickets). we can call the price per ticket "p" and the # of tickets "x". revenue is therefore px. use "y" for the net profit as stated by the problem. expenses are a flat $1,200. therefore the equation becomes:

y = px - 1200

at 200 tickets they had expenses of 1,200 and a net profit of 12,000. plugging these into the profit equation, 12,000 = p(200) - 1,000

solve for p, the price per ticket.

once you have the price per ticket you can plug it back into the equation y = px - 1200 to get the completed equation.