To find the maximum number of shares Bethany can buy with $3000, we need to divide her money by the price of one share. We can use the following formula:

Plugging in the given values, we get:

Since we need to round to the nearest whole number, we can use the rule that if the decimal part is less than 0.5, we round down, and if it is greater than or equal to 0.5, we round up. In this case, the decimal part is 0.64, more significant than 0.5, so we round up to get 205.
Therefore, the maximum number of shares Bethany can buy with $3000 is 205.