Question

The school that Castel goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 5 adult tickets and 1 child ticket for a total of $79. The school took in $135 on the second day by selling 5 adult tickets and 5 child tickets. Find the price of an adult ticket and the price of a child ticket.

Answer 1

The price of an adult ticket is $13 and the price of a child ticket is $14.

Step-by-step explanation:

To find the price of an adult ticket and the price of a child ticket, we can set up a system of equations. Let's assign variables to the unknowns:

Let x be the price of an adult ticket

Let y be the price of a child ticket

From the information given:

1. On the first day, 5 adult tickets and 1 child ticket were sold for a total of $79. This can be represented as the equation 5x + 1y = 79.
2. On the second day, 5 adult tickets and 5 child tickets were sold for a total of $135. This can be represented as the equation 5x + 5y = 135.

We can solve this system of equations using substitution or elimination method:

Multiplying the first equation by 5, we get:

25x + 5y = 395

Subtracting the second equation from this, we get:

(25x + 5y) - (5x + 5y) = 395 - 135

Simplifying, we have:

20x = 260

Dividing both sides by 20, we find:

x = 13

Substituting this value of x into one of the original equations (let's use 5x + 1y = 79), we can solve for y:

5(13) + 1y = 79

65 + y = 79

Subtracting 65 from both sides, we get:

y = 14

Therefore, the price of an adult ticket is $13 and the price of a child ticket is $14.