Question

A class went on a field trip to see a play. Adult tickets cost $18 each and student tickets cost $12 each. There were 27 more students than adults that went to the play. If the trip cost $384 in all, how many adults and students went to see the play?

Answer 1

Answer: 29 students and 2 adults went to the play

Explanation:

You know that:

• Adult tickets = $18
• Student tickets = $12
• There were 27 more students than adults
• The trip cost, 384 total

You want to know: how many adults and students went?

This is a system of equations

Defining your variables:

• A = number of adults that went
• S = number of students that went

Setting up what you know in an equation:

• 18A + 12S = 384 --> This equation represents that 18 dollars per adult, 12 dollars per student, cost a total of 384 dollars
• S = 27 + A --> This equation represents there were 27 more students than adults

You can use either the substitution or elimination method, but in this case, it is easier to use substitution because the variable "S" is already isolated.

Since S = 27+A, use that variable and plug this into your other equation to have one equation using ONLY one variable:

18A + 12(27+A) = 384

18A + 324 + 12A = 384

18A + 12A = 384-324

30A = 60

A = 2

This means there were two adults that went. Well now solve for the number of students using S = 27 + A

S = 27 + 2

S = 29

This means 29 students and 2 adults went to the play

You can check your work my making sure it fits the parameters of the problem (if it's a realistic answer) and by plugging both answers into either equation to see if it is the same answer.

• 18A + 12S = 384

18(2) + 12(29) = 394

36 + 348 = 394 --> which is accurate

Therefore the answer 29 students and 2 adults went to the play is correct