A local club is hosting a party at the school gym. Seeking to establish a connection with the community, the club will be providing a fun event and a meal for the children. The doors open at 6:00 P. M. and the games begin at 6:30 P. M. PartAPart AAs the assistant to the party director, you are instructed to split the children into groups so there is an equal number of children in each group. Each group must also have the same number of children from each age range. At 6:00 P. M., what is the greatest number of groups that can be created? How many children of each age range are represented in each group?

PartBPart BAdditional children arrive at 6:30 P. M. What is the greatest number of groups that can be created using the same guidelines in Part A?

PartCPart CThe students begin to play games. Each game takes 10 minutes to complete. There are five game stations, so five games can be played at once. Based on your answer to Part B, how long will it take all the groups to play every game? Explain your answer.

PartDPart DEach child receives a meal, which consists of a hamburger, a bag of pretzels, and a drink for the children ages 6-10 and a hamburger, two bags of pretzels, and a drink for the children that are older than 10. It costs the club $0.80 for each hamburger, $0.35 for each bag of pretzels, and $0.60 for each drink. Calculate the cost to feed each age group, as well as the total cost to feed all the children.