The first person pays $99.00 for her tickets plus $3.00 for a program each game.
The equation that represents this scenario is:
[tex]y_1=99.00+3.00\cdot x[/tex]Where x is the number of games and y is the amount paid.
Now, the second person pays $14.00 for a ticket every game, thus the equation that represents this situation is:
[tex]y_2=14.00\cdot x[/tex]When they have paid the same amount it means y1=y2. Then equal both equations and solve for x:
[tex]\begin{gathered} 99.00+3.00x=14.00x \\ \text{Subtract 3.00x from both sides} \\ 99.00+3.00x-3.00x=14.00x-3.00x \\ 99.00=11x \\ \text{Divide both sides by 11:} \\ \frac{99.00}{11}=\frac{11x}{11} \\ 9=x \end{gathered}[/tex]Therefore, in 9 games they will have paid the same amount.
