Our goal here is to translate the given information into mathematical expressions which relate the variables to one another. Once we have the expressions, we can solve them simultaneously to find the cost of a premium ticket.
We can use p to represent premium tickets and o to represent ordinary tickets. Since a premium ticket is $20 more than the ordinary ticket:
p = o + 20
o = p − 20
Now since the students buy three premium and two ordinary tickets, we can multiply these quantities by p and o in order to equate it to the total amount they spend:
3p + 2o = 110
We now have a system of equations that we can solve by substitution or combination. If we plug the value of o, p−20, into the latter equation, we get:
3p + 2(p − 20) = 110
Multiplying through the parentheses, we get:
3p + 2p − 40 = 110
Solving for p:
5p = 150
Dividing both sides by 5 to get p:
5p5 = 1505
p = 30
.The correct answer is (D).