Question

1. the school that imani goes to is selling tickets to the annual talent show. on the first day of ticket sales the school sold 3 adult tickets and 4 student tickets for a total of $50. the school took in $35 on the second day by selling 3 adult tickets and 1 student ticket. find the price of an adult ticket and the price of a student ticket. a) adult ticket: $9, student ticket: $2 b) adult ticket: $5, student ticket: $10 c) adult ticket: $10, student ticket: $5 d) adult ticket: $6, student ticket: $8 e) adult ticket: $13, student ticket: $4

Explanation:

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

Step 1: Set up the equations

From the first day: \( 3x + 4y = 50 \)
From the second day: \( 3x + y = 35 \)

Step 2: Subtract the second equation from the first

\( (3x + 4y) - (3x + y) = 50 - 35 \)
\( 3x + 4y - 3x - y = 15 \)
\( 3y = 15 \)

Step 3: Solve for \( y \)

\( y = \frac{15}{3} = 5 \)

Step 4: Substitute \( y = 5 \) into the second equation

\( 3x + 5 = 35 \)
\( 3x = 35 - 5 = 30 \)

Step 5: Solve for \( x \)

\( x = \frac{30}{3} = 10 \)

So the adult ticket is $10 and the student ticket is $5, which corresponds to option C.

Answer:

C. adult ticket: $10, student ticket: $5