document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182928>Question 1182928</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Imagine that the price per gallon of gas with a $7 car wash is $3.19 and the price without the car wash is $3.39.  When is it worth it to buy the car wash?  When is it worth it if the car wash costs $2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813061 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=813061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> price per gallon of gas with 7 dollar car wash is 3.19.<BR>\n" );
document.write( "price per gallon of gas without the car wash is 3.39.\r<BR>\n" );
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document.write( "y = total price<BR>\n" );
document.write( "x = number of gallons of gas.<BR>\n" );
document.write( "price of car wash is 7.00.\r<BR>\n" );
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document.write( "total cost with car wash is y = 7 + 3.19 * x<BR>\n" );
document.write( "total cost without car wash is y = 3.39 * x\r<BR>\n" );
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document.write( "it is worth it to buy the car wash when the total price with the car wash is less than the total price without the car wash.\r<BR>\n" );
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document.write( "the inequality for that is:\r<BR>\n" );
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document.write( "7 + 3.19 * x < 3.39 * x\r<BR>\n" );
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document.write( "subtract 3.19 * x from both sides of that equation to get:<BR>\n" );
document.write( "7 <= 3.39 * x - 3.19 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "7 < .20 * x<BR>\n" );
document.write( "divide both sides by .2 to get:<BR>\n" );
document.write( "7/.20 < x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "35 < x<BR>\n" );
document.write( "this is the same as:<BR>\n" );
document.write( "x > 35\r<BR>\n" );
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document.write( "if the number of gallons of gas is greater than 35, then it is cheaper to buy the gas with the car wash than without.\r<BR>\n" );
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document.write( "if you buy exactly 35 gallons of gas, you will pay the same for with the car wash and without the car wash.<BR>\n" );
document.write( "7.00 + 3.19 * 35 = 118.65<BR>\n" );
document.write( "3.39 * x = 118.65.\r<BR>\n" );
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document.write( "if you buy 30 gallons of gas, you will pay less for without the car wash than with the car wash.<BR>\n" );
document.write( "7.00 + 3.19 * 30 = 102.7<BR>\n" );
document.write( "3.39 * 30 = 101.7\r<BR>\n" );
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document.write( "if you buy 40 gallons of gas, you will pay less for with the car wash than without the car wash.<BR>\n" );
document.write( "7.00 + 3.19 * 40 = 134.6<BR>\n" );
document.write( "3.39 * 40 = 135.6\r<BR>\n" );
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document.write( "if the car wash costs 2 dollars instead of 7, then the equations are:\r<BR>\n" );
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document.write( "y = 2 + 3.19 * x for with the car wash.<BR>\n" );
document.write( "y = 3.39 * x for without the car wash.\r<BR>\n" );
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document.write( "the total cost for with the car wash will be less than the total cost without the car wash when 2.00 + 3.19 * x <= 3.39 * x\r<BR>\n" );
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document.write( "subtract 3.19 * x from both sides to get:<BR>\n" );
document.write( "2 < .20 * x<BR>\n" );
document.write( "divide both sides by .2 to get:<BR>\n" );
document.write( "2/.2 < x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "10 < x<BR>\n" );
document.write( "this is the same as x > 10\r<BR>\n" );
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document.write( "the break even point is when x = 10<BR>\n" );
document.write( "you pay less without the car wash when x < 10<BR>\n" );
document.write( "you pay less with the car wash when x > 10\r<BR>\n" );
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document.write( "when x = 10, you pay the same with or without the car wash.<BR>\n" );
document.write( "2 + 3.19 * 10 = 33.9<BR>\n" );
document.write( "3.39 * 10 = 33.9\r<BR>\n" );
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document.write( "when x = 9, you pay less without the car wash.<BR>\n" );
document.write( "2 + 3.19 * 9 = 30.71<BR>\n" );
document.write( "3.39 * 9 = 30.51\r<BR>\n" );
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document.write( "when x = 11, you pay less with the car wash.<BR>\n" );
document.write( "2 + 3.19 * 11 = 37.09<BR>\n" );
document.write( "3.39 * 11 = 37.29<BR>\n" );
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