Word Problem help please

[pathaniaus]

There are 6 stores in town that had a total of 20 visitors on a particular day. However, only 10 people went shopping that day; some people vistsed more than one store. If 6 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?

[DanaJ]

So 6 people of the 10 that visited stores are on the clear, so to speak. Since the 6 visited two stores each, then they count for 12 of the total number of visitors, or 12 out of 20.
The four people that are left are your "tools", so to speak. Since each and every one of the shoppers visited at least one store, you'll consider the worst case scenario for three of these remaining fellows, in that they only visited one store each. This makes for another 3 visitors, to add to the 12 already calculated for the total of 15 out of 20. This leaves 5 "visitor" spots for the last one of the 4 people.

I'm actually pretty curious about the OA for this one. Word problems are not my strong point and it's almost midnight here...

[jba05d]

DanaJ

I obtained the same answer as you did. I believe 5 is the correct number. Out methodology was completely the same.

[pathaniaus]

that is correct. 5 visits for the last person. Thank you for the very clear explanation. That really helped.