Question

1. brendas school is selling tickets to a spring musical. on the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. the school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. what is the price of one senior citizen ticket and one child ticket?

Explanation:

Step1: Define variables for ticket prices

Let $s$ = price of senior ticket, $c$ = price of child ticket.

Step2: Set up equations from sales data

First day: $3s + 9c = 75$
Second day: $8s + 5c = 67$

Step3: Simplify first equation

Divide by 3: $s + 3c = 25$, rearrange to $s = 25 - 3c$

Step4: Substitute $s$ into second equation

$8(25 - 3c) + 5c = 67$
Expand: $200 - 24c + 5c = 67$
Simplify: $200 - 19c = 67$

Step5: Solve for $c$

$-19c = 67 - 200$
$-19c = -133$
$c = \frac{-133}{-19} = 7$

Step6: Solve for $s$ using $c=7$

$s = 25 - 3(7) = 25 - 21 = 4$

Answer:

The price of one senior citizen ticket is $\$4$, and the price of one child ticket is $\$7$.