The school that Alberto goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 6 senior citizen tickets and 2 child tickets for a total of $96. The school took in
$120 on the second day by selling 6 senior citizen tickets and 4 child tickets. Find the price of a
senior citizen ticket and the price of a child ticket.

The price of both tickets is $12 each

Step-by-step explanation:

System of Equations

Let's call:

x = price of a senior citizen ticket

y = price of a child ticket.

On the first day of ticket sales, the school sold 6 senior citizen tickets and 2 child tickets for $96. Setting up the first equation:

6x + 2y = 96

Dividing by 2:

3x +  y = 48         [1]

On the second day, the school sold 6 senior citizen tickets and 4 child tickets for $120:

6x + 4y = 120

Dividing by 2:

3x + 2y = 60         [2]

Subtracting [2] and [1]:

2y - y = 60 - 48

y = 12

From [1]:

3x +  12 = 48

3x = 48 - 12 = 36

x = 36/3 = 12

x = 12

The price of both tickets is $12 each

irrational, cannot