Question

A charity organization had a fundraiser where they sold each ticket 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 $1,200. 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.

Answer 1

Answer: y = 66x - 1200

Explanation: The charity organisation has to sell a number of tickets to cover their production costs of $1,200. It is given that after selling 200 tickets they retain a net profit of $12,000. Net profit is deduced as: Total sales - total costs. Sales is calculated as total tickets x selling price per ticket.

If we let b represent the sales earned from selling tickets, then:

Net profit = total sales - total costs

12,000 = 200b - 1,200

We can then solve for b by taking the 1200 to the other side of the equal sign. When we do that the sign of that number changes. This is also the same as adding 1200 to both sides of the equal sign:

∴12000 + 1200 = 200b

13200 = 200b

To get the price of one single ticket, b, we need to divide both sides by 200.

∴ b = 66

This means that each ticket's selling price is $66.

So when when we take it back to the calculation of net profit then it becomes:

Net profit = total sales - total costs

y = 66x - 1200

To test:

y = 66x - 1200

= 66 (200 tickets) - 1200

= $12,000

Answer 2

Answer:

b = 66

Explanation:

b will be represent the sales earned from selling tickets:

Net profit = total sales - total costs

Net profit is 12,000

Total sales is 200b

Total costs is 1,200

Put them together and then you get:

12,000 = 200b - 1,200

Change the minus sign in the equation to an addition sign so now it's:

12000 + 1200 = 200b

Now add it:

13200 = 200b

Now divide to get b alone

13200 = 200b

/200       /200

The answer:

66 = b

So now we get the price if you were to buy 1 ticket