document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190610>Question 190610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> # 2. Make a conjecture about the relationship between the original number and the final number in the following process.\r<BR>\n" );
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document.write( "Pick a number.<BR>\n" );
document.write( "Multiply the number by 5<BR>\n" );
document.write( "Add 10 to the product<BR>\n" );
document.write( "Divide the sum by 5<BR>\n" );
document.write( "Subtract 1 from the quotient  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143069 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=143069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 2\r<BR>\n" );
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document.write( "Q: <font color=red> Make a conjecture about the relationship between the original number and the final number in the following process.\r<BR>\n" );
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document.write( "Pick a number.<BR>\n" );
document.write( "Multiply the number by 5<BR>\n" );
document.write( "Add 10 to the product<BR>\n" );
document.write( "Divide the sum by 5<BR>\n" );
document.write( "Subtract 1 from the quotient  </font>\r<BR>\n" );
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document.write( "A:\r<BR>\n" );
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document.write( "Let \"x\" be the unknown number\r<BR>\n" );
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document.write( "Example # 1\r<BR>\n" );
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document.write( "Step 1) \"Pick any number\". I choose the number 3\r<BR>\n" );
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document.write( "Step 2) \"...multiply the number by 5\". 3*5 = 15\r<BR>\n" );
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document.write( "Step 3) \"Add 10 to the product\". 15 + 10 = 25\r<BR>\n" );
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document.write( "Step 4) \"Divide the sum by 5\". 25/5 = 5\r<BR>\n" );
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document.write( "Step 5) \"Subtract 1 from the quotient\". 5 - 1 = 4\r<BR>\n" );
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document.write( "So after picking the number 3, the result after all of these operations is 4\r<BR>\n" );
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document.write( "Example # 2\r<BR>\n" );
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document.write( "Step 1) \"Pick any number\". I choose the number 13\r<BR>\n" );
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document.write( "Step 2) \"...multiply the number by 5\". 13*5 = 65\r<BR>\n" );
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document.write( "Step 3) \"Add 10 to the product\". 65 + 10 = 75\r<BR>\n" );
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document.write( "Step 4) \"Divide the sum by 5\". 75/5 = 15\r<BR>\n" );
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document.write( "Step 5) \"Subtract 1 from the quotient\". 15 - 1 = 14\r<BR>\n" );
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document.write( "So after picking the number 13, the result after all of these operations is 14\r<BR>\n" );
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document.write( "Example # 3\r<BR>\n" );
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document.write( "Step 1) \"Pick any number\". I choose the number 21\r<BR>\n" );
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document.write( "Step 2) \"...multiply the number by 5\". 21*5 = 105\r<BR>\n" );
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document.write( "Step 3) \"Add 10 to the product\". 105 + 10 = 115\r<BR>\n" );
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document.write( "Step 4) \"Divide the sum by 5\". 115/5 = 23\r<BR>\n" );
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document.write( "Step 5) \"Subtract 1 from the quotient\". 23 - 1 = 22\r<BR>\n" );
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document.write( "So after picking the number 23, the result after all of these operations is 22\r<BR>\n" );
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document.write( "Are you starting to see the pattern?\r<BR>\n" );
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document.write( "Example # 4\r<BR>\n" );
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document.write( "Step 1) \"Pick any number\". I choose the number 9\r<BR>\n" );
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document.write( "Step 2) \"...multiply the number by 5\". 9*5 = 45\r<BR>\n" );
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document.write( "Step 3) \"Add 10 to the product\". 45 + 10 = 55\r<BR>\n" );
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document.write( "Step 4) \"Divide the sum by 5\". 55/5 = 11\r<BR>\n" );
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document.write( "Step 5) \"Subtract 1 from the quotient\". 11 - 1 = 10\r<BR>\n" );
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document.write( "So after picking the number 9, the result after all of these operations is 10\r<BR>\n" );
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document.write( "Notice how whatever number we choose, the result is simply the next number. \r<BR>\n" );
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document.write( "Conjecture: If our number is \"x\", then the result of these operations is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here's what's happening algebraically:\r<BR>\n" );
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document.write( "Step 1) \"Pick any number\". I choose the number \"x\"\r<BR>\n" );
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document.write( "Step 2) \"...multiply the number by 5\". x*5 = 5x\r<BR>\n" );
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document.write( "Step 3) \"Add 10 to the product\". 5x+10 \r<BR>\n" );
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document.write( "Step 4) \"Divide the sum by 5\". <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B10%29%2F5=%285%28x%2B2%29%29%2F5=%28cross%285%29%28x%2B2%29%29%2Fcross%285%29=x%2B2 ALIGN=MIDDLE  ALT=\"%285x%2B10%29%2F5=%285%28x%2B2%29%29%2F5=%28cross%285%29%28x%2B2%29%29%2Fcross%285%29=x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 5) \"Subtract 1 from the quotient\". <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29-1=x%2B2-1=x%2B1 ALIGN=MIDDLE  ALT=\"%28x%2B2%29-1=x%2B2-1=x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So after choosing the number \"x\", the result is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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