SOLUTION: answer for one video club charges $25 to become a member and $2.50 to rent each video another charges no rental fee and $3.25 to rent each video how many videos must you rent to ma

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Question 120132: answer for one video club charges $25 to become a member and $2.50 to rent each video another charges no rental fee and $3.25 to rent each video how many videos must you rent to make the first club more economical
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let C represent the total cost of renting x number of videos.
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For the video club that charges a $25 fee to join, the cost will be that $25 plus an additional
charge of $2.50 times the number of videos rented (x videos). So the total cost of renting can be
written in equation form as:
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C = 2.50*x + 25
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The other video club just charges $3.50 for each video that is rented. So the total cost
to rent x videos is just $3.50 times x. In equation form this is:
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C = 3.50*x
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The "break-even" point occurs when the two costs are equal. If the two costs are equal, then
the right sides of the two equations are equal. Set them equal and you have:
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2.50*x + 25 = 3.50*x
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You can solve this equation by first collecting the x-terms on one side of the equation. To
do this, get rid of the 2.50*x on the left side by subtracting 2.50*x from both sides of
the equation. When you do that subtraction you end up with:
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25 = 1.0*x or just 25 = x
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This tells you that when you rent 25 videos the cost is the same for each club. After that,
the cost will be less for the club with the $25 fee, because each video rental beyond 25 rentals
will cost $2.50 ... but each video beyond 25 in the other club will always cost $3.50 no matter
how many you rent.
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You can also see this if you graph the two equations. The graph below has the rental cost
on the y-axis and the number of rentals along the x-axis. The "red" graph shows the cost of
renting tapes from the club that has the $25 fee. The green graph shows the cost of renting
tapes from the club that charges $3.50 for each rental.
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graph%28600%2C600%2C-5%2C50%2C-5%2C200%2C2.5x%2B25%2C3.5x%29
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Note that out to 25 on the x axis, the green graph is below the red graph. That means the total
cost of getting up to 25 rentals will be lower than the cost of renting from the club with the
$25 fee. For more than 25 rentals (on the x-axis) the total cost of the red graph will
be lower than the total cost of the green graph. Therefore, the cost will be less for the
club with the $25 fee (shown by the red graph being lower than the green graph).
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Hope this helps you to understand the problem.
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