document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172306>Question 1172306</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Bob spent 50 dollars on pens and markers. The ratio of money spent on pens pencils and markers was 4:5:1. Pens were sold at 3 for a dollar. The number of pencils he bought was 1/6 of the number of pens. The number of markers he bought was 2/5 of the number of pencils. <BR>\n" );
document.write( "How many pens and markers did he buy.<BR>\n" );
document.write( "How many pencils could he buy for 175 dollars. Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797300 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=797300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's break up the problem into these known facts:<ul><li>Fact 1: Bob spent 50 dollars on pens and markers. </li><li>Fact 2: The ratio of money spent on pens pencils and markers was 4:5:1. </li><li>Fact 3: Pens were sold at 3 for a dollar. </li><li>Fact 4: The number of pencils he bought was 1/6 of the number of pens. </li><li>Fact 5: The number of markers he bought was 2/5 of the number of pencils.</li></ul>Let x be some positive real number.<BR>\n" );
document.write( "Fact 2 says the ratio of money spent on pens, pencils and markers is 4:5:1. <BR>\n" );
document.write( "This means <BR>\n" );
document.write( "4x dollars spent on pens<BR>\n" );
document.write( "5x dollars spent on pencils<BR>\n" );
document.write( "1x dollars spent on markers<BR>\n" );
document.write( "The ratio 4x:5x:1x reduces to 4:5:1\r<BR>\n" );
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document.write( "So we have<BR>\n" );
document.write( "4x+1x = 5x dollars<BR>\n" );
document.write( "spent on pens and markers.\r<BR>\n" );
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document.write( "From fact 1, we know this figure is 50 dollars. So,<BR>\n" );
document.write( "5x = 50<BR>\n" );
document.write( "5x/5 = 50/5<BR>\n" );
document.write( "x = 10\r<BR>\n" );
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document.write( "With this x value, we find that:<BR>\n" );
document.write( "4x = 4*10 = 40 dollars spent on pens<BR>\n" );
document.write( "5x = 5*10 = 50 dollars spent on pencils<BR>\n" );
document.write( "1x = 1*10 = 10 dollars spent on markers\r<BR>\n" );
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document.write( "40+50+10 = 100 dollars was spent overall\r<BR>\n" );
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document.write( "Pens were sold at 3 for a dollar (fact 3)\r<BR>\n" );
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document.write( "We can form these series of equations<BR>\n" );
document.write( "3 pens = 1 dollar<BR>\n" );
document.write( "6 pens = 2 dollars<BR>\n" );
document.write( "9 pens = 3 dollars<BR>\n" );
document.write( "12 pens = 4 dollars<BR>\n" );
document.write( "And so on\r<BR>\n" );
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document.write( "The left side is triple that of the right side. \r<BR>\n" );
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document.write( "In general we have <BR>\n" );
document.write( "3y pens = y dollars<BR>\n" );
document.write( "where y is some nonnegative real number<BR>\n" );
document.write( "We'll further say<BR>\n" );
document.write( "y = amount of money spent on pens\r<BR>\n" );
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document.write( "Whatever dollar amount (y) you spent on pens, the number of pens you get is triple of that (3y)<BR>\n" );
document.write( "So p = 3y where p is the number of pens\r<BR>\n" );
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document.write( "In the previous section, we found that $40 was spent on pens.<BR>\n" );
document.write( "Use y = 40 to find p<BR>\n" );
document.write( "p = 3y<BR>\n" );
document.write( "p = 3*40<BR>\n" );
document.write( "p = 120\r<BR>\n" );
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document.write( "So 120 pens were purchased.\r<BR>\n" );
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document.write( "Earlier we defined p as the number of pens. <BR>\n" );
document.write( "Let's make c and m the number of pencils and markers. \r<BR>\n" );
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document.write( "In other words,<BR>\n" );
document.write( "p = number of pens<BR>\n" );
document.write( "c = number of pencils<BR>\n" );
document.write( "m = number of markers<BR>\n" );
document.write( "all of these values are nonnegative whole numbers\r<BR>\n" );
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document.write( "From fact 4, we know that,<BR>\n" );
document.write( "c = (1/6)*p<BR>\n" );
document.write( "c = p/6<BR>\n" );
document.write( "c = 120/6 ... plug in p = 120<BR>\n" );
document.write( "c = 20<BR>\n" );
document.write( "Bob purchased 20 pencils\r<BR>\n" );
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document.write( "And from fact 5, we can say,<BR>\n" );
document.write( "m = (2/5)*c<BR>\n" );
document.write( "m = (2/5)*20 ... plug in c = 20<BR>\n" );
document.write( "m = 0.4*20<BR>\n" );
document.write( "m = 8<BR>\n" );
document.write( "He also bought 8 markers\r<BR>\n" );
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document.write( "We have this summary<BR>\n" );
document.write( "120 pens purchased<BR>\n" );
document.write( "20 pencils purchased<BR>\n" );
document.write( "8 markers purchased\r<BR>\n" );
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document.write( "This shows he bought 120+8 = 128 pens and markers\r<BR>\n" );
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document.write( "That wraps up the first question.\r<BR>\n" );
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document.write( "Now onto the second question.\r<BR>\n" );
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document.write( "Recall earlier that $100 was spent overall. <BR>\n" );
document.write( "Let's bump this up to $175\r<BR>\n" );
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document.write( "The ratio 4x:5x:1x would then lead us to<BR>\n" );
document.write( "4x+5x+1x = 175<BR>\n" );
document.write( "10x = 175<BR>\n" );
document.write( "x = 175/10<BR>\n" );
document.write( "x = 17.5\r<BR>\n" );
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document.write( "This means<BR>\n" );
document.write( "4x = 4*17.5 = 70 <BR>\n" );
document.write( "dollars is spent on pens\r<BR>\n" );
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document.write( "Then y = 70 leads to<BR>\n" );
document.write( "p = 3y<BR>\n" );
document.write( "p = 3*70<BR>\n" );
document.write( "p = 210<BR>\n" );
document.write( "210 pens were purchased\r<BR>\n" );
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document.write( "And,<BR>\n" );
document.write( "c = p/6<BR>\n" );
document.write( "c = 210/6<BR>\n" );
document.write( "c = 35<BR>\n" );
document.write( "35 pencils were purchased\r<BR>\n" );
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document.write( "Final Summary:\r<BR>\n" );
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document.write( "Question: How many pens and markers did he buy?<BR>\n" );
document.write( "<font color=red>Answer: 128</font>\r<BR>\n" );
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document.write( "Question: How many pencils could he buy for 175 dollars?<BR>\n" );
document.write( "<font color=red>Answer: 35</font><BR>\n" );
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