Question

1. the school that laura goes to is selling tickets to the annual talent show. the school took in $55 on the first day by selling 4 senior citizen tickets, 2 adult tickets and 5 child. the school took in $67 on the second day by selling 7 senior citizen tickets, 2 adult tickets and 5 child tickets. on the third day the show earned $46 when they sold 2 senior citizen tickets, 4 adult tickets and 2 child tickets. what is the price of an adult ticket?

$11
$4
$7
$5

Explanation:

Step1: Define Variables

Let \( s \) = price of senior ticket, \( a \) = price of adult ticket, \( c \) = price of child ticket.

Step2: Set Up Equations

First day: \( 4s + 2a + 5c = 55 \)
Second day: \( 7s + 2a + 5c = 67 \)
Third day: \( 2s + 4a + 2c = 46 \) (simplify: \( s + 2a + c = 23 \))

Step3: Subtract First from Second

\( (7s + 2a + 5c) - (4s + 2a + 5c) = 67 - 55 \)
\( 3s = 12 \) → \( s = 4 \)

Step4: Substitute \( s = 4 \) into First Equation

\( 4(4) + 2a + 5c = 55 \) → \( 16 + 2a + 5c = 55 \) → \( 2a + 5c = 39 \) (Equation 1)

Step5: Substitute \( s = 4 \) into Simplified Third Equation

\( 4 + 2a + c = 23 \) → \( 2a + c = 19 \) (Equation 2)

Step6: Subtract Equation 2 from Equation 1

\( (2a + 5c) - (2a + c) = 39 - 19 \)
\( 4c = 20 \) → \( c = 5 \)

Step7: Substitute \( s = 4 \), \( c = 5 \) into Equation 2

\( 2a + 5 = 19 \) → \( 2a = 14 \) → \( a = 7 \)

Answer:

\$7