Question

A hockify season ticket holder pays $99.00 for her tickets plus $3.00 for a program each game. A secondperson pays $14.00 for a ticket to every game, but doesn't buy programs. In how many games will they havepaid the same amount?0 33O 6O 8O 9

Answer 1

The first person pays $99.00 for her tickets plus $3.00 for a program each game.

The equation that represents this scenario is:

`y_1=99.00+3.00\cdot x`

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:

`y_2=14.00\cdot x`

When they have paid the same amount it means y1=y2. Then equal both equations and solve for x:

`\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:} \\ (99.00)/(11)=(11x)/(11) \\ 9=x \end{gathered}`

Therefore, in 9 games they will have paid the same amount.