It costs 261 for 3 nights at pavia pavilion hotels at the same rate how much will it cost to stay for 7 nights.

There's two ways I can see someone doing this:

The first way requires you to work out the price of 1 night, and multiply that price by 7. So you would do 261 ÷ 3 = 87 (price) and 3 ÷ 3 = 1 (nights). So now you know that per night, it costs 87. Multiply this by 7 to get 609 as the total for 7 nights.

The second method requires you to work out 7 ÷ 3, which is 2.33333333... Multiply 261 by 2.33333333 to work out how much it is for 7 nights. (Also 609). 

The first method however is a lot simpler and sometimes more accurate, because as we found in this example, we didn't encounter any decimals to get the answer. 

Whose mistake? can you give more details to what the question is asking?