Question

Cedar Point Amusement Park charges $51.99 for an adult admission and $26.99 for a junior admission. One Thursday, the park collected $15,591.40 from a total of 360 adults and juniors. How many admissions of each type were sold?

Answer 1

The total price must equal the total earned from adults and the total earned from children:
51.99x + 26.99y = 15,591.4

Since we can't work with two variables, we simplify the equation by turning the second variable into a relation to the first. We know that the number of adults must add to the number of children to equal 360:
x + y = 360
x = 360 - y

Now we plug the 'x' into the equation:
51.99(360-y) + 26.99y = 15,591.4
18,716.4 - 51.99y + 26.99y = 15,591.4
18,716.4 - 25y = 15,591.4
3,125 - 25y = 0
3,125 = 25y
y = 125 children tickets sold

Now we plug in y into the equation we made earlier:
x + 125 = 360
x = 235 adult tickets sold

Answer 2

Admissions sold Unit cost total cost
Adult 235 51.99 12,217.65
Junior 125 26.99 3,373.75
Total 360 15,591.40

Given:
Total number of people = 360
No. of Adults = x
No. of juniors = 360 - x
Adult admission = 51.99
Junior admission = 26.99
Total admission = 15,591.40

51.99x + 26.99(360-x) = 15,591.40
51.99x + 9716.40 - 26.99x = 15,591.40
25x = 15,591.40 - 9,716.40
25x = 5,875
x = 5,875/25
x = 235 *No. of Adults

No. of Juniors = 360 - x = 360 - 235 = 125