Question

Chandler Heisinger buys a monthly metro card, which entitles him to unlimited subway travel in New York City, for $81 per month. Without the MetroCard, each subway ride costs $2. How many rides per month would Chandler have to take so that the cost of he rides with the MetroCard is less than the cost of the rides without the MetroCard?

Answer 1

Let $r$ 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 $2r$. 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,
$81\ \textless \ 2r \\ r\ \textgreater \ 81/2\ \textgreater \ 40 \\ r \geq 41$
Thus, at a minimum, Chandler must take 41 rides for his MetroCard to be cheaper than not having it.