The corporate team-building event will cost $36 if it has 18 attendees. How many attendees can there be, at most, if the budget for the corporate team-building event is $78?

Question

Isaiah Anthony · Accepted Answer

Using a sort of cheat method!

For $78 the count of attendees is 39

#color(blue)("The cheating method - Not really a cheat!")# Consider the attendance for $36 to be an attendance of I set The count of sets for $78 is #78/36# So the count of attendees is #78/36xx18=39# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("The long way round")# Using a ratio, but this isn't a fraction; it's in fraction format Let the unknown count be #x# Initial condition:#->18/($36)# Target condition:#->x/($78)# Since the numerical ratios in every instance are the same, we can write: #("count")/("cost")->18/(36)-=x/78# Add 78 to both sides. #color(green)(18/36color(red)(xx78)" "=" "x/78color(red)(xx78))# The procedure behind canceling out is as follows: #color(green)(39" "=" "x xx(color(red)(78))/78)# But #78/78=1# and #1xx x=x# #"count "=x=39#

Eva Abramson · Answer

undefined The maximum number of attendees for the corporate team-building event with a budget of $78 is 39 attendees.