Question

The directors of the Ashborne Community Center are raising money for a new outreach

program. To meet their goal of $2,400, they are selling tickets to an event hosted by a local
celebrity. They know from previous fundraisers that the expression -4p +220 can be used to
estimate the number of tickets they will sell based on the price per ticket, p.
What two ticket prices will make the community center exactly $2,400 in revenue?

Answer 1

15 or 40

Explanation:

Answer 2

• $15
• $40

Explanation:

You want to know the ticket prices that will achieve the revenue goal of $2400 if the number of tickets sold at price p is (220 -4p).

Revenue

The revenue from sales is the product of the number of tickets sold and their price:

r(p) = p(220 -4p)

We want this value to be 2400:

p(220 -4p) = 2400

p² -55p +600 = 0 . . . . . . divide by 4, put in standard form

Factoring

Some ways to factor 600 are ...

600 = 10(60) = 12(50) = 15(40) = 20(30)

We want a pair of factors that have a total of 55. Those are 15 and 40. This lets us factor the quadratic as ...

(p -15)(p -40) = 0

Solutions are the values of p that make these factors zero:

p -15 = 0 ⇒ p = 15

p -40 = 0 ⇒ p = 40

The ticket prices that will make $2400 in revenue are $15 or $40.

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