document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189270>Question 1189270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> As part of boosting your health this time of pandemic, you ask your parent if you could enroll at a Zumba class that was held online. Your parent agreed to it and the Zumba instructor said that she charges according to the number of participants. This is the list of charges that she said,if there are 20 participants or below, the instructor charges ₱400.00 for each participant per month. If the number of participant is between 20 and 30, she charges ₱350.00 for each participant per month. If there are 30 participants or more she charges ₱300.00 for each participants per month. Write the piecewise function that describes what the instructor charges . </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820624 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820624\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE C(x) = \left\{400 \ \text{ if } 0 \le x \le 20\\350 \ \text{ if } 20 < x < 30\\300 \ \text{ if } x \ge 30\\ \right. \"><BR>\n" );
document.write( "x = number of students<BR>\n" );
document.write( "C(x) = monthly cost for any one student\r<BR>\n" );
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document.write( "How to get that answer:\r<BR>\n" );
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document.write( "The first line represents the portion <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C=+20 ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, ie when x is between 0 and 20 inclusive of both endpoints. If x is in this interval, then we can say C(x) = 400 since the teacher charges ₱400 when having between 0 and 20 students. This represents the cost for a single student (ie the amount the parent would pay if x fits the criteria). All throughout this sub interval, we have the cost stay the same.\r<BR>\n" );
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document.write( "Or if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%3C+x+%3C+30 ALIGN=MIDDLE  ALT=\"20+%3C+x+%3C+30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then we go for the middle option <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29+=+350 ALIGN=MIDDLE  ALT=\"C%28x%29+=+350\"   DISABLED_style= \"max-width:90%; height:auto;\" > (it's ₱50 cheaper per student in this interval). The reasoning is similar, but the interval is different this time of course. \r<BR>\n" );
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document.write( "Or, we have one final option, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=30 ALIGN=MIDDLE  ALT=\"x%3E=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29+=+300 ALIGN=MIDDLE  ALT=\"C%28x%29+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is another ₱50 cheaper\r<BR>\n" );
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document.write( "So in short, the amount charged will have 3 tiers of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C=+20 ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%3C+x+%3C+30 ALIGN=MIDDLE  ALT=\"20+%3C+x+%3C+30\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=30 ALIGN=MIDDLE  ALT=\"x%3E=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > which correspond to the charges of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400 ALIGN=MIDDLE  ALT=\"400\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=350 ALIGN=MIDDLE  ALT=\"350\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300 ALIGN=MIDDLE  ALT=\"300\"   DISABLED_style= \"max-width:90%; height:auto;\" > in that order.<BR>\n" );
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