Question

The school that Ashley goes to is selling tickets to the annual dance competition. On the first day of ticket sales, the school sold 5 adult tickets and 7 child tickets for a total of $152. On the second day, the school took in $86 by selling 5 adult tickets and 1 child ticket. Find the price of an adult ticket and the price of a child ticket.

a. Adult ticket: $6, Child ticket: $5
b. Adult ticket: $15, Child ticket: $11
c. Adult ticket: $10, Child ticket: $6
d. Adult ticket: $17, Child ticket: $12

Answer 1

To find the price of an adult ticket and the price of a child ticket, we can set up and solve a system of equations using the given information. The price of an adult ticket is $15 and the price of a child ticket is $11.

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 based on the given information.

Let's denote the price of an adult ticket as x and the price of a child ticket as y.

From the first day of ticket sales, we have the equation:

5x + 7y = 152

From the second day of ticket sales, we have the equation:

5x + y = 86

Now, we can solve this system of equations to find the values of x and y.

Multiplying the second equation by 7 and subtracting it from the first equation, we get:

(5x + 7y) - (35x + 7y) = 152 - (602)

-30x = -450

x = 15

Substituting this value of x into the second equation, we get:

5(15) + y = 86

75 + y = 86

y = 11

Therefore, the price of an adult ticket is $15 and the price of a child ticket is $11.