Afamily of 5 comes to the amusement park. there are two adults and three children (under the age of 12). they qualify for a special family rate of $174.45. the clerk tells them that a child's ticket always costs $11 less than an adult's ticket. how much is each adult ticket and how much is each child's ticket?

In the problem above, let x be the cost of ticket for adults. Based on the description stated by the clerk, each child's ticket costs x - 11.

The total cost of the ticket is $174.45 and may be used to get the value of x. The equation is, 
  
                                     2x + 3(x - 11) = 174.45

Solving x in the equation gives x = 41.49 and x -11 = 30.49. Thus, each adult's ticket cost $41.49 and child's ticket costs $30.49.