A theatre production company donated free tickets for their show to the local Boys & Girls club. They claimed that the ticket value was $306. A child's ticket cost $5.25 and an adult ticket cost $9.75. If there were three times as many children's tickets as adult tickets, how many adults and children got to attend the show for free?
adults --- x
children -- 3x
solve:
975x + 525(3x) = 30600
1500x
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the number of adult tickets is 'x' and the number of child tickets is '3x' (since there were three times as many child tickets as adult tickets).
The cost of an adult ticket is $9.75, so the cost of 'x' adult tickets would be 9.75x.
The cost of a child ticket is $5.25, so the cost of '3x' child tickets would be 5.25 * 3x = 15.75x.
According to the problem, the theater company claimed that the total value of the tickets donated was $306. So we can set up the equation:
9.75x + 15.75x = 306
Now, we can solve for 'x':
25.5x = 306
x = 306 / 25.5
x = 12
Now that we know the value of 'x', we can find the number of adults and children who attended the show for free:
Number of adult tickets = x = 12
Number of child tickets = 3x = 3 * 12 = 36
Therefore, 12 adults and 36 children got to attend the show for free.