Question

The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate his abilities. He charges $200 for these events, and the club is charging $1.50 for tickets with a chance to have the psychic read the ticket holder’s mind. Let x represent the number of tickets sold and y represent money.a. How much would the club gain or lose by selling 100 tickets?b. How many tickets are needed to break even? (Round to nearest whole ticket.)

Answer 1

Given:

$200 - payment for the self-proclaimed psychic

$1.50 - club's earnings for each ticket

Find: club's gain/lose after selling 100 tickets and number of tickets in order to break-even

Solution:

Since x = represents the number of tickets sold, we can say that the profit of the club is y = ($1.50 times the number of tickets x sold) - the payment for the psychic.

`y=1.50x-200`

a. Let's plugin x = 100 tickets in the formula above.

`y=1.50(100)-200`

Then, solve.

`\begin{gathered} y=150-200 \\ y=-50 \end{gathered}`

Since the answer is negative, by selling 100 tickets, the club loses $50.

b. Break-even means there is no gain nor lose. Hence, the charge and the earnings of the club are equal. So, with this, we will assume that y = 0.

`0=1.50x-200`

Then, we can solve for x or the number of tickets needed.

Add 200 on both sides of the equation.

`\begin{gathered} 0+200=1.50x-200+200 \\ 200=1.50x \end{gathered}`

Divide both sides by 1.50.

`\begin{gathered} (200)/(1.50)=(1.50x)/(1.50) \\ 133.33=x \\ 133\approx x \end{gathered}`

Hence, the club needs to sell 133 tickets in order to break even.