Question

A total of 937 people attended the play. Admission was $2.00 for adults and $0.75 for students. The total ticket sales amounted to $1,109. How many students and adults attended the school play? First complete the equations below, where A stands for Adults and S stands for Students. 2A + 0.755 = 1,109; A + S = 937 Now use the equations to find the number of students and adults. Students = [?]; Adults = [ ] ​

Answer 1

612 students and 325 adults.

Explanation:

To determine the number of adults and students who attended the event, knowing that in total there were 937 people who spent a total of $ 1,109 and that each student ticket is worth $ 0.75 while each adult ticket is worth $ 2, the following logical reasoning must be performed:

2 - 0.75 = 1.25

Therefore, the minimum that each ticket will be worth is $ 0.75, while there will be a surplus of money that will be divisible by 1.25, which is the amount of more that each adult paid on their ticket.

Therefore, since 0.75 x 937 equals 702.75, the total price surplus is 406.25 (1,109 - 702.75). Now, this number divided by 1.25 gives a total of 325, with which 325 adults attended the event. In turn, given that the total number of attendees was 937, the total number of students who attended the event is 612 (937 - 325).