Question

the school that stefan goes to is selling tickets to a choral performance. on the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. the school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. find the price of a senior citizen ticket and the price of a child ticket.

Explanation:

Step1: Define variables for ticket prices

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

Step2: Set up equations from sales data

First day: $3s + c = 38$
Second day: $3s + 2c = 52$

Step3: Subtract first equation from second

$(3s + 2c) - (3s + c) = 52 - 38$
$c = 14$

Step4: Substitute $c$ into first equation

$3s + 14 = 38$
$3s = 38 - 14$
$3s = 24$
$s = \frac{24}{3} = 8$

Answer:

The price of a senior citizen ticket is $\$8$, and the price of a child ticket is $\$14$.