Question

1. the school that julia goes to is selling tickets to a play. on the first day of ticket sales the school sold 3 adult tickets and 3 student tickets for a total of $33. the school took in $48 on the second day by selling 3 adult tickets and 6 student tickets. find the price of an adult ticket and the price of a student ticket.

a) adult ticket: $6, student ticket: $5 b) adult ticket: $5, student ticket: $6
c) adult ticket: $3, student ticket: $3 d) adult ticket: $3, student ticket: $2
e) adult ticket: $8, student ticket: $6

Explanation:

Step1: Define variables

Let \( x \) be the price of an adult ticket and \( y \) be the price of a student ticket.

Step2: Set up equations

From the first day: \( 3x + 3y = 33 \), simplify to \( x + y = 11 \) (Equation 1).
From the second day: \( 3x + 6y = 48 \), simplify to \( x + 2y = 16 \) (Equation 2).

Step3: Solve the system

Subtract Equation 1 from Equation 2: \( (x + 2y) - (x + y) = 16 - 11 \)
\( x + 2y - x - y = 5 \)
\( y = 5 \)
Substitute \( y = 5 \) into Equation 1: \( x + 5 = 11 \)
\( x = 11 - 5 = 6 \)

Answer:

A) adult ticket: $6, student ticket: $5