document.write( "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 \n" ); document.write( "
Algebra.Com's Answer #88120 by bucky(2189)\"\" \"About 
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Let C represent the total cost of renting x number of videos.
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\n" ); document.write( "For the video club that charges a $25 fee to join, the cost will be that $25 plus an additional
\n" ); document.write( "charge of $2.50 times the number of videos rented (x videos). So the total cost of renting can be
\n" ); document.write( "written in equation form as:
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\n" ); document.write( "C = 2.50*x + 25
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\n" ); document.write( "The other video club just charges $3.50 for each video that is rented. So the total cost
\n" ); document.write( "to rent x videos is just $3.50 times x. In equation form this is:
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\n" ); document.write( "C = 3.50*x
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\n" ); document.write( "The \"break-even\" point occurs when the two costs are equal. If the two costs are equal, then
\n" ); document.write( "the right sides of the two equations are equal. Set them equal and you have:
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\n" ); document.write( "2.50*x + 25 = 3.50*x
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\n" ); document.write( "You can solve this equation by first collecting the x-terms on one side of the equation. To
\n" ); document.write( "do this, get rid of the 2.50*x on the left side by subtracting 2.50*x from both sides of
\n" ); document.write( "the equation. When you do that subtraction you end up with:
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\n" ); document.write( "25 = 1.0*x or just 25 = x
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\n" ); document.write( "This tells you that when you rent 25 videos the cost is the same for each club. After that,
\n" ); document.write( "the cost will be less for the club with the $25 fee, because each video rental beyond 25 rentals
\n" ); document.write( "will cost $2.50 ... but each video beyond 25 in the other club will always cost $3.50 no matter
\n" ); document.write( "how many you rent.
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\n" ); document.write( "You can also see this if you graph the two equations. The graph below has the rental cost
\n" ); document.write( "on the y-axis and the number of rentals along the x-axis. The \"red\" graph shows the cost of
\n" ); document.write( "renting tapes from the club that has the $25 fee. The green graph shows the cost of renting
\n" ); document.write( "tapes from the club that charges $3.50 for each rental.
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\n" ); document.write( "\"graph%28600%2C600%2C-5%2C50%2C-5%2C200%2C2.5x%2B25%2C3.5x%29\"
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\n" ); document.write( "Note that out to 25 on the x axis, the green graph is below the red graph. That means the total
\n" ); document.write( "cost of getting up to 25 rentals will be lower than the cost of renting from the club with the
\n" ); document.write( "$25 fee. For more than 25 rentals (on the x-axis) the total cost of the red graph will
\n" ); document.write( "be lower than the total cost of the green graph. Therefore, the cost will be less for the
\n" ); document.write( "club with the $25 fee (shown by the red graph being lower than the green graph).
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\n" ); document.write( "Hope this helps you to understand the problem.
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