document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205543>Question 205543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve\r<BR>\n" );
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document.write( "Bayside Insurance offers two health plans. Under Plan A, Sam would have to pay the first $170 of his medical bills, plus 35% of the rest. Under Plan B, Sam would pay the first $210, but only 30% of the rest. For what amount of medical bills will Plan B save Sam money? Assume he was over $210 in bills. Sam would save with Plan B if he had more than $_____ in bills. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155176 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=155176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem:<BR>\n" );
document.write( "Bayside Insurance offers two health plans. Under Plan A, Sam would have to pay the first $170 of his medical bills, plus 35% of the rest. Under Plan B, Sam would pay the first $210, but only 30% of the rest. For what amount of medical bills will Plan B save Sam money? Assume he was over $210 in bills. Sam would save with Plan B if he had more than $_____ in bills.<BR>\n" );
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document.write( "let x = cost of sam's medical bills.<BR>\n" );
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document.write( "Under Plan A, Sam pays 170 + .35 * (x - 170)<BR>\n" );
document.write( "Under Plan B, Sam pays $210 + .3 * (x - 210)<BR>\n" );
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document.write( "Assume x > $210<BR>\n" );
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document.write( "Break even point is when Plan A costs the same as plan B.<BR>\n" );
document.write( "This happens when:<BR>\n" );
document.write( "170 + .35*(x-170) = 210 + .3*(x-210)<BR>\n" );
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document.write( "removing the parentheses, this equation becomes:<BR>\n" );
document.write( "170 + .35x - 59.5 = 210 + .3x - 63<BR>\n" );
document.write( "simplifying, this becomes:<BR>\n" );
document.write( "110.5 + .35x = 147 + .3x<BR>\n" );
document.write( "subtracting 110.5 from both sides and subtracting .3x from both sides of the equation gets:<BR>\n" );
document.write( ".35x - .3x = 147 - 110.5<BR>\n" );
document.write( "simplifying gets:<BR>\n" );
document.write( ".05x = 36.5<BR>\n" );
document.write( "dividing both sides of the equation by .05 gets:<BR>\n" );
document.write( "x = 730<BR>\n" );
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document.write( "testing by substituting in the break even equation gets:<BR>\n" );
document.write( "170 + .35*(730-170) = 210 + .3*(730-210)<BR>\n" );
document.write( "removing parentheses gets:<BR>\n" );
document.write( "170 + 255.5 - 59.5 = 210 + 219 - 63<BR>\n" );
document.write( "simplifying gets:<BR>\n" );
document.write( "366 = 366<BR>\n" );
document.write( "confirming that the value of x is good.<BR>\n" );
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document.write( "Answer to your question is:<BR>\n" );
document.write( "Sam would save with plan B is Sam had more than $730 in bills.<BR>\n" );
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document.write( "As a test, assume Sam has $750 in bills.<BR>\n" );
document.write( "Under plan A Sam would pay:<BR>\n" );
document.write( "170 + .35*(750 - 170) = 170 + .35 * (580) = 170 + $203 = $373<BR>\n" );
document.write( "Under plan B Sam would pay:<BR>\n" );
document.write( "210 + .3*(750-210) = 210 + .3 * (540) = 210 + 162 = $372<BR>\n" );
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document.write( "The numbers might be smaller but you could test with as little as a penny over the break even point.<BR>\n" );
document.write( "To make it reasonable, we'll use $1.00 over the break even point.<BR>\n" );
document.write( "Assume the bills were $731.<BR>\n" );
document.write( "Under Plan A Sam would pay $170 + (.35)*($731-$170) = $170 + .35*561 = $366.35<BR>\n" );
document.write( "Under Plan B Sam would pay $210 + (.3)*($731-$210) = $210 + .34*521 = $366.30<BR>\n" );
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document.write( "A graph of both equations would show this.<BR>\n" );
document.write( "Below $730 Plan A should be cheaper.<BR>\n" );
document.write( "Above $730 Plan B should be cheaper.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28600%2C600%2C-100%2C1500%2C-50%2C800%2C170+%2B+.35%28x-170%29%2C210+%2B+.3%28x-210%29%2C1000000%2F%28x-730%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "when x = 0, plan A intersects the y axis at 110.5<BR>\n" );
document.write( "when x = 0, plan B intersect the y axis at 147.00<BR>\n" );
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document.write( "you can see that plan A is cheaper than plan B up to x = $731 and then becomes more expensive.<BR>\n" );
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document.write( "You could have worked this directly by making the plan b equation less than the plan a equation rather than equal.  <BR>\n" );
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document.write( "if you did that you would have had:<BR>\n" );
document.write( "210 + .3*(x - 210) < 170 + .35*(x - 170)<BR>\n" );
document.write( "you solve in the same way but you're dealing with an inequality now and the inequality rules prevail.<BR>\n" );
document.write( "first thing is to remove the parentheses.<BR>\n" );
document.write( "equation becomes:<BR>\n" );
document.write( "210 + .3x - (.3*210) < 170 + .35x - (.35*170)<BR>\n" );
document.write( "subtracting 170 from both sides and subtracting .3x from both sides and adding (.35*170) to both sides gets:<BR>\n" );
document.write( "210 - 170 - (.3*210) + (.35*170) < .35x - .3x<BR>\n" );
document.write( "combining like terms gets:<BR>\n" );
document.write( "40 - (.3*210) + (.35*170) < .05x<BR>\n" );
document.write( "simplifying further gets:<BR>\n" );
document.write( "40 - 63 + 59.5 < .05x<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "36.5 < .05x<BR>\n" );
document.write( "dividing both sides by .05 gets:<BR>\n" );
document.write( "36.5/.05 < x<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "730 < x<BR>\n" );
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document.write( "730 < x is the same as x > 730 so the result of this equation is x > 730.<BR>\n" );
document.write( "when x is greater than 730 plan b is cheaper.<BR>\n" );
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document.write( "this is the same result we got earlier so it confirms the results and was more direct because the inequality equation rather than the break even equation was used.<BR>\n" );
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document.write( " </SPAN>\n" );
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