Question

1. asanjis school is selling tickets to a fall musical. on the first day of ticket sales the school sold 12 adult tickets and 8 student tickets for a total of $184. the school took in $176 on the second day by selling 13 adult tickets and 4 student tickets. what is the price each of one adult ticket and one student ticket?

Explanation:

Step1: Define Variables

Let \( a \) be the price of one adult ticket (in dollars) and \( s \) be the price of one student ticket (in dollars).

Step2: Set Up Equations

From the first day: \( 12a + 8s = 184 \).
From the second day: \( 13a + 4s = 176 \).

Step3: Simplify Equations

Simplify the first equation by dividing by 4: \( 3a + 2s = 46 \) (Equation 1).
Multiply the second equation by 2: \( 26a + 8s = 352 \) (Equation 2).

Step4: Eliminate \( s \)

Subtract Equation 1 multiplied by 4 (\( 12a + 8s = 184 \)) from Equation 2:
\( (26a + 8s) - (12a + 8s) = 352 - 184 \)
\( 14a = 168 \)
\( a = 12 \).

Step5: Find \( s \)

Substitute \( a = 12 \) into Equation 1: \( 3(12) + 2s = 46 \)
\( 36 + 2s = 46 \)
\( 2s = 10 \)
\( s = 5 \).

Answer:

The price of one adult ticket is \$12, and the price of one student ticket is \$5.