Chapter 9.7, Problem 5CYU

To determine

Solve the ticket prices.

Answer to Problem 5CYU

4

Explanation of Solution

Given Information: $y=-x^2+8x$ and $y=-20+9x$ where $x$ is ticket price in dollars

Formula Used: Factorization

Calculation:

Revenue for a school play: $y=-x^2+8x$

Cost to produce the school play: $y=-20+9x$

where $x$ is ticket price in dollars

Ticket price that will allow the school play to break even. So,

  $-x^2+8x=-20+9x$

So, simplify

  $x^2-8x+9x=20$

So,

  $x^2+x-20=0$

Now, factorize

  $x^2+5x-4x-20=0$

So,

  $x\left(x+5\right)-4\left(x+5\right)=0$

Now,

  $\left(x-4\right)\left(x+5\right)=0$

Hence,

  $x=4$ or $x=-5$

So, ticket price in dollar $x=4$