Let [tex]r[/tex] be the number of rides Chandler takes in a month. Then the cost with the MetroCard is still $81, but the cost without the MetroCard is [tex]2r[/tex]. So we can set up an equation representing what we want: "The cost with a MetroCard of r rides in a month is less than the cost without a MetroCard." In equations,
[tex]81\ \textless \ 2r \\ r\ \textgreater \ 81/2\ \textgreater \ 40 \\
r \geq 41[/tex]
Thus, at a minimum, Chandler must take 41 rides for his MetroCard to be cheaper than not having it.
