Visitors to a carnival can buy an unlimited-ride pass for $50 or an entrance-only pass for $20. In one day, 282 passes were sold for a total of $10,680. How many unlimited-ride passes were sold?
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
