Question

Tazewell High School decided to take their students on a field trip to the movie theater. A total of 250 people went on the trip. Adults pay $4.50 for a ticket and students pay $2.50 for a ticket. How many students and how many adults went to the movies if they paid a total of $805 at the movie theater?

Answer 1

Solve this by a system of equations: one equation to represent the NUMBER of people who went and the other to represent the MONEY spent to go. So designate the adults as A, for example, and the students as S. The number of adults, A, plus the number of students, S, was 250. So that's our first equation: A + S = 250.

Answer 2

Refer to the attachment.

Answer 3

Now do the money thing. Adults cost $4.50 each so adults is represented as 4.5A. Students cost $2.50 each, so students is represented as 2.5S. The amount of money earned was $805. So the money from adults, 4.5A, plus the money from students, 2.5S = 805. That's our second equation. So they are both:

Answer 4

A + S = 250
4.5A + 2.5S = 805

Answer 5

I recommend solving this by substitution. From the first equation, A = 250 - S. So sub that into the second equation, as such:
4.5(250 - S) + 2.5S = 805
1125 - 4.5S + 2.5S = 805
1125 - 2S = 805
-2S = 805 - 1125
-2S = -320
S = 160
That means that there were 160 students. If there were 160 students, then 250 - 160 = 90 Adults. See that?

Answer 6

yes

Answer 7

I get it now, thank you.

Answer 8

You're welcome. Thank you for the medal!