document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090246>Question 1090246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kate is planning on going to the pool a lot this summer. It costs $5 to go each time, but Kate noticed that the pool also offers a Summer Discount Card and a Summer Flat Rate Card. The Discount card costs $50 but would allow her to go to the pool for only $2 each time. The Flat Rate card costs $200 but would let her in to the pool for free all summer.<BR>\n" );
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document.write( "a. What factors will be most important when Kate is deciding to buy the Discount card, the Flat Rate card, or neither?<BR>\n" );
document.write( "b. Write an equation for each of the three scenarios. Explain your thinking.<BR>\n" );
document.write( "c. Graph your equations in a graphing utility or in a calculator. What does the $\footnotesize{x}$-axis represent? What does the $\footnotesize{y}$-axis represent?<BR>\n" );
document.write( "d. What do the intersection points of the lines represent?<BR>\n" );
document.write( "e. Decide which plan you think is the best and explain why. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704732 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Kate is planning on going to the pool a lot this summer. It costs $5 to go each time, but Kate noticed that the pool also offers a Summer Discount Card and a Summer Flat Rate Card. The Discount card costs $50 but would allow her to go to the pool for only $2 each time. The Flat Rate card costs $200 but would let her in to the pool for free all summer.<BR>\n" );
document.write( " $$<BR>\n" );
document.write( " a. What factors will be most important when Kate is deciding to buy the Discount card, the Flat Rate card, or neither?<BR>\n" );
document.write( " How many times will she be going to the pool this summer.<BR>\n" );
document.write( ":<BR>\n" );
document.write( " b. Write an equation for each of the three scenarios. Explain your thinking.<BR>\n" );
document.write( "let t = no. of time she went to the pool<BR>\n" );
document.write( "f(t) = the total cost for the summer<BR>\n" );
document.write( " f(t) = 5t; no card<BR>\n" );
document.write( " f(t) = 2t + 50, discount card<BR>\n" );
document.write( " f(t) = 200, flat rate card<BR>\n" );
document.write( ":<BR>\n" );
document.write( " c. Graph your equations in a graphing utility or in a calculator. What does the $\footnotesize{x}$-axis represent? What does the $\footnotesize{y}$-axis represent?<BR>\n" );
document.write( "vertical axis = total cost<BR>\n" );
document.write( "horizontal axis = no. of pool visits<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+50%2C+-100%2C+300%2C+5x%2C+2x%2B50%2C+200%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+50%2C+-100%2C+300%2C+5x%2C+2x%2B50%2C+200%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "f(t) = 5t; red<BR>\n" );
document.write( "f(t) = 2t+50; green<BR>\n" );
document.write( "f(t) = 200; blue<BR>\n" );
document.write( ": <BR>\n" );
document.write( " d. What do the intersection points of the lines represent?<BR>\n" );
document.write( "At the intersections, the no. of visits the cost is the same<BR>\n" );
document.write( " At 16 visits, the no card and discount card cost $80 & $82$<BR>\n" );
document.write( " At 17+ visits, the discount card is a better deal, $85 & $84<BR>\n" );
document.write( "and<BR>\n" );
document.write( " At 40 visits, no card (40*5) and flat rate are the same.<BR>\n" );
document.write( " After 40 the flat rate is a far better deal<BR>\n" );
document.write( ": <BR>\n" );
document.write( " e. Decide which plan you think is the best and explain why.<BR>\n" );
document.write( "If you are determined to become a much better swimmer, and have the $,<BR>\n" );
document.write( "take the flat rate. An added incentive to go often to get your money's worth. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Did all this make sense to you? A good problem to think about, don't you think? CK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );