Question

ex 5. joe is selling tickets to a concert. on the first day of ticket sales he sold 3 senior citizen tickets and 1 child ticket for a total of $38. the second day of ticket sales he sold 3 senior citizen tickets and 2 child tickets for a total of $52. find the price of a senior citizen ticket and a child ticket.

Explanation:

Step1: Define variables

Let \( s \) be the price of a senior citizen ticket and \( c \) be the price of a child ticket.
From the first day: \( 3s + 1c = 38 \) (Equation 1)
From the second day: \( 3s + 2c = 52 \) (Equation 2)

Step2: Subtract Equation 1 from Equation 2

\( (3s + 2c) - (3s + c) = 52 - 38 \)
Simplify: \( 3s + 2c - 3s - c = 14 \)
Which gives: \( c = 14 \)

Step3: Substitute \( c = 14 \) into Equation 1

\( 3s + 14 = 38 \)
Subtract 14 from both sides: \( 3s = 38 - 14 = 24 \)
Divide by 3: \( s = \frac{24}{3} = 8 \)

Answer:

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