document.write( "Question 285801: A standard train ticket in a certain city costs $2.00 per ride. People who use the train also have the option of purchasing a frequent rider pass for $15.75 each month. With the pass a ticket costs only $1.25 per ride. Use an inequality to determine the number of train rides in a month for which purchasing the monthly pass is more economical than purchasing the standard train ticket. \n" ); document.write( "
Algebra.Com's Answer #207218 by Theo(13342)![]() ![]() You can put this solution on YOUR website! x = number of rides per month.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Without the pass, the cost per ride is 2.00 per ride.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "With the pass, the cost per ride is 1.25 per ride plus 15.75 per month.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "You want to know at what number of rides does the cost per ride using the pass become cheaper than the cost per ride without using the pass.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The formula for total cost is as follows:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "without the pass:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "C1 = 2*x\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "with the pass:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "C2 = 15.75 + 1.25*x\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "You want to know when C2 becomes less than C1.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "C2 < C1 is the inequality equation you are looking for.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Since C2 = 15.75 + 1.25*x, and C1 = 2*x, this equation becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "15.75 + 1.25*x < 2*x\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Subtract 1.25*x from both sides of this equation to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "15.75 < 2*x - 1.25*x which becomes:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "15.75 < .75*x\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Divide both sides of this equation by .75*x to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "15.75/.75 < x\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Simplify to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "21 < x\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "21 < x is the same as x > 21.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Your answer is the C2 becomes cheaper than C1 when x > 21.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "If you make x = 21, then:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "C1 = 2*21 = 42 \n" ); document.write( "C2 = 15.75 + 1.25*21 = 15.75 + 26.25 = 42\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "They are equal.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "If you make x = 22, then:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "C1 = 2*22 = 44 \n" ); document.write( "C2 = 15.75 + 1.25*22 = 15.75 + 27.5 = 43.25\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "43.25 is cheaper than 44 so C2 is cheaper than C1, confirming that the equation is good.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |