Question

1.Suppose a group of 24 people bought tickets to the American Kennel Club Museum of the Dog. Tickets cost $15 each for adults, $10 each for students, and $5 each for children under age 12. There were twice as many adults as children under age 12. If the total cost of the tickets was $260, how many tickets were purchased for children under age 12? * 4 tickets 6 tickets 12 tickets 8 tickets

Answer 1

Answer: 4 tickets for children under 12.

Step-by-step explanation:

A is the number of adults, S is the number of students and C is the number of children.

We have the equations:

1)  A + S + C = 24.

2) A = 2*C

3) A*$15 + S*$10 + C*$5 = $260

So we have 3 equations and 3 variables.

First, we can replace A in both of the other equations.

1) 2*C + S + C = 24

   S + 3*C = 24

and

3)  (2*C)*$15 + S*$10 + C*$5 = $260

    C*($30 + $5) + S*$10 = $260

    C*$35 + S*$10 = $260

Now, we should isolate S in the first equation, and get:

1) S = 24 - 3*C

now we can replace it on the other equation:

3) C*$35 + S*$10 = $260

   C*$35 + (24 - 3*C)*$10 = $260

   C*($35 - $30) + $240 = $260

   C*$5 = $20

    C = 20/5 = 4

So we have 4 children.