Question

1. the school that jill goes to is selling tickets to a spring musical. on the first day of ticket sales the school sold 2 senior citizen tickets and 6 student tickets for a total of $40. the school took in $84 on the second day by selling 6 senior citizen tickets and 6 student tickets. find the price of a senior citizen ticket and the price of a student ticket. a) senior citizen ticket: $11, student ticket: $3 b) senior citizen ticket: $9, student ticket: $5 c) senior citizen ticket: $9, student ticket: $4 d) senior citizen ticket: $10, student ticket: $1 e) senior citizen ticket: $3, student ticket: $11

Explanation:

Step1: Define variables

Let \( x \) be the price of a senior citizen ticket and \( y \) be the price of a student ticket.

Step2: Set up equations

From the first day: \( 2x + 6y = 40 \)
From the second day: \( 6x + 6y = 84 \)

Step3: Subtract the first equation from the second

\( (6x + 6y) - (2x + 6y) = 84 - 40 \)
\( 4x = 44 \)
\( x = 11 \)

Step4: Substitute \( x = 11 \) into the first equation

\( 2(11) + 6y = 40 \)
\( 22 + 6y = 40 \)
\( 6y = 18 \)
\( y = 3 \)

Answer:

A) senior citizen ticket: $11, student ticket: $3