Question

A hockey season ticket holder pays $77.52 for her tickets plus $6.00 for a program each game. A secondperson pays $18.92 for a ticket to every game, but doesn't buy programs. In how many games will they havepaid the same amount?0 4O 130 5O 6

Answer 1

Let x be the number of programs the first person has gone to, then the total amount paid is:

$T=77.52+6x\text{.}$

The total amount for x games that the second person paid is:

$Total=18.92x\text{.}$

Let t be the number of games that are needed so that both persons pay the same amount, then we can set the following equation:

$77.52+6t=18.92t\text{.}$

Solving the above equation for t we get:

$\begin{gathered} 77.52=18.92t-6t, \\ 77.52=12.92t, \\ \frac{77.52}{12.92}=t, \\ 6=t\text{.} \end{gathered}$

Answer:

$6.$