MHB -act.63 cost per game with season pass

[karush]

Armin is trying to decide whether to buy a season pass to his college basketball team's 20 home games this season.
The cost of an individual ticket is \$14, and the cost of a season pass is \$175.
The season pass will admit Armin to any home basketball game at no additional cost.
What is the minimum number of home basketball games Armin must attend this season
in order for the cost of a season pass to be less than the total cost of buying an individual ticket for each game he attends?

$a.\ {8}\quad b.\ {9}\quad c.\ {12}\quad d.\ {13}\quad e.\ {20}$

Spoiler: solution

$\begin{array}{lll}
\dfrac{\textit{season pass}}
{\textit{games attende}}&=\textit{cost per game}\\ \\
\dfrac{175}{13}
&=13.46
&\textit{games where cost per game is less with season pass}\\ \\
\dfrac{175}{12}
&=14.58
\end{array}$

OK the question is a somewhat tricky and hopefully the solution is quick way to solve it
Not sure if I would call this an observation question only

ck for typos thanks

 

[skeeter]

let $g \le 20$ be the number of games ...

$14g > 175 \implies g > \dfrac{175}{14} \implies g > 12.5 \implies g \ge 13$

 

[karush]

yeah that's a better way to approach it