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
