Question

A charity organization had a fundraiser where each ticket was sold for a fixed price. They had to sell a few tickets just to cover necessary production costs of $1200\$1200 $1200 dollar sign, 1200 . After selling 200200 200 200 tickets, they had a net profit of $12,000\$12{,}000 $12,000 dollar sign, 12, comma, 000 . Let P(n)P(n) P(n) P, left parenthesis, n, right parenthesis denote the net profit from the fundraiser PP P P (measured in dollars) as a function of the number of tickets sold nn n n . Write the function's formula

Answer 1

P(n)=66n-1200
12000+1200=13200,
13200/200+66,
it asks net profit, so you need to minus $1200 to find it.

Answer 2

`P(n)=66n-1200`

Explanation:

Let x be the revenue collected from selling each ticket.

We have been given that a charity organisation had to sell a few tickets just to cover necessary production costs of $1200. After selling 200 tickets, they had a net profit of $12,000.

Since we know that net profit is the difference between total revenue and total cost.

`\text{Net profit}=\text{Total revenue- Cost}`

We can represent our given information in an equation to find the revenue collected from each ticket:

`12000=200x-1200`

Let us solve for x by adding 1200 to both sides of equation.

`12000+1200=200x`

`13200=200x`

`x=(13200)/(200)`

`x=66`

Therefore, the revenue collected from selling each ticket is $66.

Now let us write the net profit, P(n), from fundraiser as the function of number of tickets sold,n.

The revenue from selling n tickets will be 66n.

Production costs = 1200

`P(n)=66n-1200`

Therefore, our desired function will be:
`P(n)=66n-1200`.