I have a bit of confusion from a word problem proposed in my business math course. The problem is as follows:

"A restaurant manager wants to track attendance in his restaurant. He notes that at 7PM on Monday, the attendance was 300 people out of 500 (Where 500 was the attendance the whole day). On 7PM on Tuesday, the attendance was 150 people out of 400 (where 400 was the attendance the whole day). He then says that the total percentage of people who attended at 7PM for those 2 days was:

$\frac{300 + 150}{500+400} = \frac{450}{900} = 0.50$.

What is the flaw in his approach to coming to this conclusion?

My take on this is that he seems to be adding fractions by adding the numerators and denominators together, which of course, can't be done. But, then again, he seems to be saying that total percent attended for that time period is total attended at 7PM divided by total attendance, which is perhaps correct? Hence, my confusion!

Any suggestions?



There is nothing wrong with his approach. There are $900$ people who came to the restaurant and $450$ of them are in the group of interest-those who were there at $7$PM one day or the other. It is as if he gathered all $900$ people in a room and asked those who were there at $7$ to raise a hand. There would be $450$ hands raised, $50\%$ of the crowd.


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