Respuesta :
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.
[tex]y=1.50x-200[/tex]a. Let's plugin x = 100 tickets in the formula above.
[tex]y=1.50(100)-200[/tex]Then, solve.
[tex]\begin{gathered} y=150-200 \\ y=-50 \end{gathered}[/tex]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.
[tex]0=1.50x-200[/tex]Then, we can solve for x or the number of tickets needed.
Add 200 on both sides of the equation.
[tex]\begin{gathered} 0+200=1.50x-200+200 \\ 200=1.50x \end{gathered}[/tex]Divide both sides by 1.50.
[tex]\begin{gathered} \frac{200}{1.50}=\frac{1.50x}{1.50} \\ 133.33=x \\ 133\approx x \end{gathered}[/tex]Hence, the club needs to sell 133 tickets in order to break even.
