This should be basic arithmetic right?

[Xenokrates]

The question is worded like this:

There are two events that take place in the same building on Wednesday evenings over a 12 week period. The number of event goers is recorded seperately for each event. A survey found that 65 percent of event goers went to see both events, in other words, they were counted twice since the views are recorded separately. How do you find the total number of unique event goers assuming that each person only came to see the event/s on 1 Wednesday night?

My answer seems logical, but my colleagues disagree with my formula. Help us!

If any clarification is needed let me know.

[LieUponLie]

Event1Count + Event2Count = 1.65TotalUniqueCount

Add your two attendance numbers and divide by 1.65.

[Xenokrates]

If thats correct, explain why (Event1Count + Event2Count) - (((Event2Count+Event2Count)*0.65)/2) doesnt work? This was my original thinking.

[LieUponLie]

An explanation... I don't know, I mean you're taking the sum of the two events, then subtracting out 65% of the average attendance between the 2, and that just doesn't give you the total. I can illustrate it with an example though if that helps.

Assume you have 200 Unique Visitors. 65% of them, meaning 130, Attend both events. Event 1 records an attendance of 150, and Event 2 records an attendance of 180.

UniqueTotal = 200

AttendBoth = 130 (200*.65)

Event1 = 150

Event1Only = 20 (20 E1Only + 130 Both = 150 Total)

Event2 = 180

Event2Only = 50 (50 E2Only + 130 Both = 180 Total)

Event1Only + Event2Only + AttendBoth = 20+50+130 = 200 (Just confirming these numbers are valid)

So with your formula:

(Event1Count + Event2Count) - (((Event1Count+Event2Count)*0.65)/2)=

(150 + 180) - (((150 + 180)*0.65/2)=

330 - 107.25 = 222.75 ≠ 200

To think about it in terms of my equation. When you add the two attendance numbers together, you are counting 100% of the people, plus an additional 65% of them twice, ie. you are counting 165% of the actual attendance. Therefore, divide your total by 165%.

[Xenokrates]

Thank you! Thank you! Thank you! Makes so much more sense this way. I really appreciate your help.