A transponder for a toll bridge costs $$17\mathrm{.}50.$ With the transponder, the toll is $$5$ each time you cross the bridge. The only other option is toll$-$by$-$plate, for which the toll is $$5\mathrm{.}25$ each time you cross the bridge with an additional administrative fee of $$2\mathrm{.}25$ for each crossing. How many times would you need to cross the bridge for the costs of the two toll options to be the same?

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Lets denote the number of times you need to cross t... View the full answer