Question

numbers of the wide waters Club pay $105 per summer season plus $9.50 each time they rent a boat non members must pay $14.75 each time they were about how many times would a member and a non member of to rent a boat in order to pay the same amount

Answer 1

The member pays  $9.50  to take a boat out,
plus  $105  just to be a member.

Let's call ' R ' the number of rentals

               Member Cost  =  (9.50 times R) + 105

        Non-member cost  =  (14.75 times R) .

You're interested in  when their costs are equal,
so at that point, we can write ...

           Member cost  =  non-member cost

                 9.5 R + 105  =  14.75 R

Subtract  9.5 R  from each side:  105  =  5.25 R

Divide each side by  5.25 :             20  =  R  

If you're going to rent a boat less than 20 times during the
Summer season, rent them at the non-member rate.

More than 20 times in 1 Summer, you'll save money by being
a member.  

This sounds a bit extreme to me.  If the Summer season means
ALL of May, June, July, August, and September, then you would
need to average more than one rental every 7.65 days ... a hair
more than one a week ... in order to save any money by being a
member.  I love sailboat rental, and I live just 2 miles from Lake
Michigan, but even at these prices (cheap), I would never average
a rental every week for 5 months.   So for me, there would be no
benefit in a membership ... at least not in the cost of boat rental.        

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Another way to do it, with more brain but less algebra:

Each time a member rents a boat, he pays  (14.75 - 9.50) = 5.25
LESS than a non-member would pay to rent the same boat.
But in order to get that deal, he had to pay $105 "up front", at the
beginning of the season, before he ever rented anything.

How many times does he have to 'save' $5.25 before he makes up
for the the  $105 ?

           ($105) / ($5.25)  =  20 times .

Answer 2

$105+$24.25=$129.25 that is the answer