tickets to a science exposition cost $5.75 each for students and $7.00 for adults. How many students and adults went if the ticket charge was $42.75?

Well this is a pretty fun problem that involves variables.
let's set some variables
s = students
a = adults
the total is
42.75
so let's solve for one variable
42.75 = 7.00a + 5.75s

let's just plug in a number for a I'm going to go with two and let's solve for s
42.75 = 7.00(2) +5.75s
42.75 =14.00 + 5.75s
28.75 = 5.75s
28.75/5.75 = s
5=s
so
so the amount of students and adults that can go is 2 adults and 5 students