Question

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?

Answer 1

Using a sort of cheat method!

For $78 the count of attendees is 39

Explanation:

`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 ratio but in fraction format (this is NOT a fraction)

Let the unknown count be `x`

Initial condition:`->18/($36)`

Target condition:`->x/($78)`

The ratio of the numbers in each case is the same. So we can write:

`("count")/("cost")->18/(36)-=x/78`

Multiply both sides by 78

`color(green)(18/36color(red)(xx78)" "=" "x/78color(red)(xx78))`

What follows is the process that is behind cancelling out

`color(green)(39" "=" "x xx(color(red)(78))/78)`

But `78/78=1` and `1xx x=x`

`"count "=x=39`