Using the information give, we can create two equations with two unknows as shown below:
50U+20E=10680 and
U+E=280.
Where U represents Unlimited ride passes and E represents Entrance-only passes. We can use the second equation to find the value of U in relation to E. So that U is represented as U=282-E. We then proceed to substitute E in the first equation using the value we assigned it in relation to U so that we can have only one unknown value in the equation. So 50U+20E=10680 becomes 50(282-E)+20E=10680. Simplifying this equation,
14100-50E+20E=10680. Putting the unknowns on one side we end up with 14100-10680=50E-20E. Solving for E, we end up with E=114. U can also be calculated by substituting the already known value of E in the simpler equation U=280-114. This means that the value of U is 168. So the number of unlimited passes that were sold is 168