A local theater charges $8 for adult tickets and $6 for children's tickets to a play. If a group of 24 goes to the theater and pays $164, how many of each ticket type did the group purchase?

The theater was attended by 10 adults and 14 children.

Step-by-step explanation:

As the theater charges adults $ 8 and children $ 6 for each ticket, there is a surcharge of $ 2 for each adult. Thus, given that a group of 24 people attended the theater, as a minimum (that is, if they were all children) the establishment should charge $ 144 (6 x 24). Now, since it charges $ 164, there is a difference of $ 20 (164 - 144), attributable to the surcharge paid by adults for each ticket. Thus, since this surcharge is $ 2, dividing 20 by 2 we obtain 10, which is the number of adults who attended the theater.

This is verified by the following calculation:

10 x 8 = 80

14 x 6 = 84

80 + 84 = 164

Therefore, the theater was attended by 10 adults and 14 children.