From the information given we could write the following equation:
5.75(s) + 7.00(a) = 42.75
Since there are two unknowns, we would need two equations to solve the problem. Without knowing the total tickets sold, or how many either student or adult tickets were sold, we can't write another equation, and cannot solve this the normal way. So let's try something else.
The amount of money for student tickets work out like this:
1 ticket = $5.75
2 tickets = $11.50
3 tickets = $17.25
4 tickets = $23.00
5 tickets = $28.75
Notice that the cents repeat after 4 tickets (.75, .50, .25, .00). Since the adult tickets are an even dollar amount (they end in .00) the amount of adult tickets will not add up to .75, which is in the total amount of $42.75. So we look at the amount of student tickets sold as 1 or 5 or 9, etc. Since we are dealing with a small amount, we can do this easily.
1 ticket: $42.75 - $5.75 = $37.00
5 tickets: $42.75 - $28.75 = $14.00
9 tickets: $42.75 - $51.75 = -$9.00
We don't have to go any farther since 9 student tickets are too much already. I'll let you figure out how many student (1 or 5) and adult tickets were sold.
