document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188521>Question 188521</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618594027/algebrahomeworkh>McDougal Littell Algebra 1</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Laura has $4.50 in dimes and quarters.  She has 3 more dimes than quarters.  How many quarters does she have.\r<BR>\n" );
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document.write( "How do you find two linear equations (y=mx+b), one that shows quantity of the coins.  And one that shows the amount the coins are worth.  I am suppose to use \"d\" and \"q\" to represent the dimes and quarters.  \r<BR>\n" );
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document.write( "So far I got: q=dx+3 and 4.50=qx+d<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141343 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=141343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "I have no intention of being mean about this, but you are so far off track that the only way to get you back on the right path is to start from the beginning.\r<BR>\n" );
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document.write( "When you were told to create an equation in the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = mx + b\">, you were meant to use <i>q</i> and <i>d</i> in place of the variables <i>y</i> and <i>x</i>.  I think that bit of instruction turned out to be more confusing than helpful.\r<BR>\n" );
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document.write( "Let <i>d</i> represent the number of dimes and let <i>q</i> represent the number of quarters.  We know that she has 3 more dimes than quarters.  So if you add 3 to the number of quarters you would get the number of dimes.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  d = q + 3\">\r<BR>\n" );
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document.write( "(just to keep track of the whole <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = mx + b\"> thing, notice that the equation that we just developed is in that very form if you consider the <i>d</i> to be the <i>y</i>, the understood 1 coefficient in front of the <i>q</i> to be the <i>m</i>, the <i>q</i> to be the <i>x</i>, and the 3 to be the <i>b</i>)\r<BR>\n" );
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document.write( "That takes care of the equation representing the relationship of the number of coins, so now let's look at an equation that represents the <i>value</i> of those coins.  By the way, when I do coin problems, I like to change the dollars and cents representation into just cents, that is for this problem I'm going to represent the $4.50 as 450 cents.  That will allow us to use whole number coefficients instead of decimal fractions.  I just think it is neater.  Having said that, onward.\r<BR>\n" );
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document.write( "Each dime is worth 10 cents, so <i>d</i> dimes must be worth 10<i>d</i> cents.  Similarly <i>q</i> quarters must be worth 25<i>q</i> cents.  And the total value of her money is 450 cents, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d + 25q = 450\">\r<BR>\n" );
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document.write( "Now you could put this into <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = mx + b\"> form, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d + 25q = 450 \ \ \Rightarrow\ \ 10d = -25q + 450 \ \ \Rightarrow\ \ d = -2.5q + 45\">\r<BR>\n" );
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document.write( "But I think that is just uglier than a mud fence and of no real value to solving this problem, so let's just go back to the original value equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10d + 25q = 450\">\r<BR>\n" );
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document.write( "Since we know from earlier that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d = q + 3\">, we can substitute <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q + 3\"> for  <i>d</i> in the value equation, like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10(q + 3) + 25q = 450\">\r<BR>\n" );
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document.write( "Distribute:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 10q + 30 + 25q = 450\">\r<BR>\n" );
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document.write( "Collect terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 35q = 420\">\r<BR>\n" );
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document.write( "Divide by 35:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ q = 12\">\r<BR>\n" );
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document.write( "So Laura has 12 quarters, and 12 + 3 = 15 dimes.\r<BR>\n" );
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document.write( "Check the answer.\r<BR>\n" );
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document.write( "12 quarters = <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 12 \times 25 = 300\text{ cents } = $3.00\">\r<BR>\n" );
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document.write( "15 dimes = <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 15 \times 10 = 150\text{ cents } = $1.50\">\r<BR>\n" );
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document.write( "And <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large $3.00 + $1.50 = $4.50\">.  Answer checks.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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