document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151480>Question 1151480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Smart student learning center charges students a registration  fee of $25 plus an hourly rate of $30 for after school tutoring.  Brilliant learning center charges students for after school tutoring based on the table below :<BR>\n" );
document.write( "       Brilliant student learning center<BR>\n" );
document.write( "        Hours of tutoring (x)  Total cost (y)<BR>\n" );
document.write( "         1                     $45<BR>\n" );
document.write( "         3                    $115<BR>\n" );
document.write( "         5                     $185<BR>\n" );
document.write( "         7                    $255<BR>\n" );
document.write( "If a student needs 4 hours of tutoring,  which statement is true?<BR>\n" );
document.write( "A. Smart student learning center charges$5 more than Brillant student learning center.<BR>\n" );
document.write( "B.<BR>\n" );
document.write( "Brilliant  student learning center charges $5 more than Smart student learning center.<BR>\n" );
document.write( "C.Smart student learning center charges #35 more than Brilliant student learning center.<BR>\n" );
document.write( "D. Brillant student learning center charges $35 more than Smart student learning center. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773243 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=773243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = number of hours of tutoring<BR>\n" );
document.write( "y = total cost\r<BR>\n" );
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document.write( "Smart student center learning, which I'll just abbreviate to \"Company S\", charges a registration fee of $25 plus an hourly rate of $30. This means the equation for Company S is <BR>\n" );
document.write( "y = 30x+25\r<BR>\n" );
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document.write( "Note how this equation is in the form y = mx+b<BR>\n" );
document.write( "m = slope = 30<BR>\n" );
document.write( "b = y intercept = 25<BR>\n" );
document.write( "The slope tells us how much y goes up each time x increases by 1 (ie, for each increase of 1 hour, the cost goes up by $30)<BR>\n" );
document.write( "The y intercept is the starting cost, or the cost if you have x = 0 hours of tutoring.\r<BR>\n" );
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document.write( "I'll abbreviate \"Brilliant learning center\" as \"Company B\". This company has the following table of x,y values.<BR>\n" );
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document.write( "<tr><TD >x</TD><TD >y</TD></tr>\r\n" );
document.write( "<tr><TD >1</TD><TD >45</TD></tr>\r\n" );
document.write( "<tr><TD >3</TD><TD >115</TD></tr>\r\n" );
document.write( "<tr><TD >5</TD><TD >185</TD></tr>\r\n" );
document.write( "<tr><TD >7</TD><TD >255</TD></tr>\r\n" );
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document.write( "</TABLE>\r<BR>\n" );
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document.write( "Pick two points from that table, say the first two rows<BR>\n" );
document.write( "Row1: (x1,y1) = (1, 45)<BR>\n" );
document.write( "Row2: (x2,y2) = (3, 115)\r<BR>\n" );
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document.write( "Compute the slope between those two points<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (115-45)/(2)<BR>\n" );
document.write( "m = 70/2<BR>\n" );
document.write( "m = 35<BR>\n" );
document.write( "The slope is 35, which means Company B charges $35 an hour.\r<BR>\n" );
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document.write( "Use any row of the table as the (x,y) value. I'll use row 1, so (x,y) = (1,45)<BR>\n" );
document.write( "Plug those values, along with m = 35, into the form<BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "and solve for b\r<BR>\n" );
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document.write( "y = mx+b<BR>\n" );
document.write( "45 = 35*1+b<BR>\n" );
document.write( "45 = 35+b<BR>\n" );
document.write( "45-35 = b<BR>\n" );
document.write( "10 = b<BR>\n" );
document.write( "b = 10<BR>\n" );
document.write( "The starting cost for Company B is $10, i.e. this is the registration cost or the cost of having x = 0 hours of tutoring.\r<BR>\n" );
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document.write( "Overall the equation for Company B is<BR>\n" );
document.write( "y = 35x+10\r<BR>\n" );
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document.write( "To summarize so far:\r<BR>\n" );
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document.write( "y = 30x+25 is the cost equation for Company S<BR>\n" );
document.write( "y = 35x+10 is the cost equation for Company B\r<BR>\n" );
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document.write( "From here we plug x = 4 into each equation and simplify using PEMDAS\r<BR>\n" );
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document.write( "Company S<BR>\n" );
document.write( "y = 30*x+25<BR>\n" );
document.write( "y = 30*4+25<BR>\n" );
document.write( "y = 120+25<BR>\n" );
document.write( "y = 145<BR>\n" );
document.write( "Having x = 4 hours of tutoring at Company S will cost you y = 145 dollars.\r<BR>\n" );
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document.write( "Company B<BR>\n" );
document.write( "y = 35*x+10<BR>\n" );
document.write( "y = 35*4+10<BR>\n" );
document.write( "y = 140+10<BR>\n" );
document.write( "y = 150<BR>\n" );
document.write( "Having x = 4 hours of tutoring at Company B will cost you y = 150 dollars.\r<BR>\n" );
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document.write( "We see the difference of the two companies is 150-145 = 5 dollars. So Company S is cheaper by $5. Or put another way, Company B is $5 more expensive.\r<BR>\n" );
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document.write( "-------------------------------------------\r<BR>\n" );
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document.write( "Final Answer: <BR>\n" );
document.write( "<font color=red size=4>B) Brilliant student learning center charges $5 more than Smart student learning center.</font><BR>\n" );
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