Members of the wide waters club pay $105 per summer season, plus $9.50 each tim

Members of the wide waters club pay $105 per summer season, plus $9.50 each tim

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  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.        

    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 .

  2.   20

    Step-by-step explanation:

    Let x represent the number of rentals. Then the cost will be the same when ...

      105 +9.50x = 14.75x

      105 = 5.25x

      105/5.25 = x = 20

    Each would have to rent a boat 20 times in order to pay the same amount.

  3. The difference between 9.5 and 14.75 is 5.25.
    The fee per season 105 divided by the difference (5.25) is 20. 

    14.75 x 20 = 295
    (9.5 x 20) + 105 = 295
    190 + 105 = 295

  4. The number of times members and non-members will have to rent a boat in order to pay the same amount=20

    Step-by-step explanation:

    We can have two expressions to show the total cost paid by a member and non-member;

    Total cost by member=Cost per summer season+cost per number of times they rent a boat×number of times they rent a boat

    where;

    Cost per summer season=$105

    Cost per number of times they rent a boat=$9.50

    Number of times they rent a boat=n

    Replacing;

    Total cost by a member=105+(9.5×n)=9.5 n+105equation 1

    Total cost by a non-member=Cost per number of times they rent a boat×number of times they rent a boat

    where;

    Cost per number of times they rent a boat=$14.75

    Number of times they rent a boat=n

    Replacing;

    Total cost by a non-member=(14.75×n)=14.75 nequation 2

    To calculate the number of times they would have to rent a boat in order to pay the same amount, we equate equation 1 to equation 2

    9.5 n+105=14.75 n

    14.75 n-9.5 n=105

    5.25 n=105

    n=105/5.25

    n=20

    The number of times members and non-members will have to rent a boat in order to pay the same amount=20

  5. To answer this problem, we need to make a system of equations.

    C= cost (in place of y in typical equation)
    t= number of times renting boat (in place of x in typical equation)

    Members- C=9.5t+105
    Non-Members- C=14.75t

    You can set them equal to each other because of transitive property.

    9.5t+105=14.75t
    Subtract 9.5t both sides
    105=5.25t
    Divide 5.25 on both sides
    t=20

    So it takes 20 times to rent a boat and have the same cost.

    🙂

  6. If you are looking for the equation it would be y=105+9.50x because they pay 105 no matter what and each time they visit they pay an additional 9.50

  7. Set up a problem: 105+9.50b=14.75b. Combine like terms: subtract 9.50b from both sides: 105=5.25b. Get unknown by itself: divide both sides by 5.25: 20=b. The answer is 20. They would have to rent a boat 20 times to pay the same amount. 🙂

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