document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=226300>Question 226300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joe Lick bought some 20-cent and 25-cent stamps. He bought 32 stamps in all, and paid $7.40 for them. How many stamps of each kind did he buy?\r<BR>\n" );
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document.write( "Problem Solving:Using Charts </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #168559 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=168559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Joe Lick bought some 20-cent and 25-cent stamps. He bought 32 stamps in all, and paid $7.40 for them. How many stamps of each kind did he buy?\r<BR>\n" );
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document.write( "Step 1.  Let x be the number of 20-cent stamps\r<BR>\n" );
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document.write( "Step 2.  Let 32-x be the number of 25-cent stamps since there are 32 stamps in all.\r<BR>\n" );
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document.write( "Step 3.  Let 0.20x be the dollar value of 20-cent stamps.\r<BR>\n" );
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document.write( "Step 4.  Let 0.25(32-x) be the dollar value of 25-cent stamps.\r<BR>\n" );
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document.write( "Step 5.  Then, 0.20x+0.25(32-x)=7.40 be the total dollar value of 7.40.\r<BR>\n" );
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document.write( "Step 6.  Solving the equation in Step 5 yields the following steps:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=explain_simplification.solver>EXPLAIN simplification of an expression</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><B>Your Result</B>: <BR><BR>\n" );
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document.write( "  YOUR ANSWER\n" );
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document.write( "<LI><B>This is an <A  rel=nofollow HREF=/algebra/homework/equations/>equation</A>!</B> Solutions: <FONT SIZE=+2><U><B>x=12</B></U></FONT>.<BR></LI>\n" );
document.write( "<LI><B>Graphical form</B>: <A  rel=nofollow HREF=/algebra/homework/equations/>Equation</A> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20x%2B0.25%2A%2832-x%29=7.40 ALIGN=MIDDLE  ALT=\"0.20x%2B0.25%2A%2832-x%29=7.40\"   DISABLED_style= \"max-width:90%; height:auto;\" > was fully solved.</LI><LI><B>Text form</B>: 0.20x+0.25*(32-x)=7.40 simplifies to 0=0</LI><LI><B>Cartoon (animation) form</B>: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=simplify_cartoon%28+0.20x%2B0.25%2A%2832-x%29=7.40+%29 ALIGN=MIDDLE  ALT=\"simplify_cartoon%28+0.20x%2B0.25%2A%2832-x%29=7.40+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR> For tutors: <CODE>simplify_cartoon( 0.20x+0.25*(32-x)=7.40 )</CODE></LI>\n" );
document.write( "<LI>If you have a website, here's a <A rel=nofollow  rel=nofollow HREF=/services/rendering/simplifier.mpl?expression=0.20x%2B0.25%2A%2832-x%29=7.40>link</A> to this solution. </LI>\n" );
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document.write( "<H3  DISABLED_style= \"background-color: #88ccDD; font-weight: bold; margin-top: 0px; margin-bottom: 3px; text-align: center; padding: 2px;\">DETAILED EXPLANATION</H3>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20%2Ax%2B0.25%2A%28highlight_red%28+32+%29-x%29=7.40 ALIGN=MIDDLE  ALT=\"0.20%2Ax%2B0.25%2A%28highlight_red%28+32+%29-x%29=7.40\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Moved <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right of expression <BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20%2Ax%2B0.25%2A%28-x%2Bhighlight_green%28+32+%29%29=7.40& border=1  ALIGN=MIDDLE  ALT=\"0.20%2Ax%2B0.25%2A%28-x%2Bhighlight_green%28+32+%29%29=7.40\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20%2Ax%2B0.25%2A%28-x%2B32%29=highlight_red%28+7.40+%29 ALIGN=MIDDLE  ALT=\"0.20%2Ax%2B0.25%2A%28-x%2B32%29=highlight_red%28+7.40+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Moved these terms to the left <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+-7.40+%29 ALIGN=MIDDLE  ALT=\"highlight_green%28+-7.40+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20%2Ax%2B0.25%2A%28-x%2B32%29-highlight_green%28+7.40+%29=0& border=1  ALIGN=MIDDLE  ALT=\"0.20%2Ax%2B0.25%2A%28-x%2B32%29-highlight_green%28+7.40+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20%2Ax%2Bhighlight_red%28+0.25%2A%28-x%2B32%29+%29-7.40=0 ALIGN=MIDDLE  ALT=\"0.20%2Ax%2Bhighlight_red%28+0.25%2A%28-x%2B32%29+%29-7.40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Expanded term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25 ALIGN=MIDDLE  ALT=\"0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > by using <A  rel=nofollow HREF=/algebra/homework/Distributive-associative-commutative-properties/>associative property</A> on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%2B32%29 ALIGN=MIDDLE  ALT=\"%28-x%2B32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20%2Ax-highlight_green%28+0.25%2Ax+%29%2Bhighlight_green%28+0.25%2A32+%29-7.40=0& border=1  ALIGN=MIDDLE  ALT=\"0.20%2Ax-highlight_green%28+0.25%2Ax+%29%2Bhighlight_green%28+0.25%2A32+%29-7.40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20%2Ax-0.25%2Ax%2Bhighlight_red%28+0.25%2A32+%29-highlight_red%28+7.40+%29=0 ALIGN=MIDDLE  ALT=\"0.20%2Ax-0.25%2Ax%2Bhighlight_red%28+0.25%2A32+%29-highlight_red%28+7.40+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Replace constants in expression: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+0.25%2A32+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+0.25%2A32+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+-7.40+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+-7.40+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+0.6+%29 ALIGN=MIDDLE  ALT=\"highlight_green%28+0.6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+0.6+%29%2B0.20%2Ax-0.25%2Ax=0& border=1  ALIGN=MIDDLE  ALT=\"highlight_green%28+0.6+%29%2B0.20%2Ax-0.25%2Ax=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+0.6+%29%2B0.20%2Ax-0.25%2Ax=0 ALIGN=MIDDLE  ALT=\"highlight_red%28+0.6+%29%2B0.20%2Ax-0.25%2Ax=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Moved <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6 ALIGN=MIDDLE  ALT=\"0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right of expression <BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.20%2Ax-0.25%2Ax%2Bhighlight_green%28+0.6+%29=0& border=1  ALIGN=MIDDLE  ALT=\"0.20%2Ax-0.25%2Ax%2Bhighlight_green%28+0.6+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+0.20%2Ax+%29-highlight_red%28+0.25%2Ax+%29%2B0.6=0 ALIGN=MIDDLE  ALT=\"highlight_red%28+0.20%2Ax+%29-highlight_red%28+0.25%2Ax+%29%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Eliminated <A  rel=nofollow HREF=/algebra/homework/expressions/>similar terms</A> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+0.20%2Ax+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+0.20%2Ax+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+-0.25%2Ax+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+-0.25%2Ax+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  replacing them with  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+%280.20-0.25%29%2Ax+%29 ALIGN=MIDDLE  ALT=\"highlight_green%28+%280.20-0.25%29%2Ax+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+%280.20-0.25%29%2Ax+%29%2B0.6=0& border=1  ALIGN=MIDDLE  ALT=\"highlight_green%28+%280.20-0.25%29%2Ax+%29%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight_red%28+0.20+%29-highlight_red%28+0.25+%29%29%2Ax%2B0.6=0 ALIGN=MIDDLE  ALT=\"%28highlight_red%28+0.20+%29-highlight_red%28+0.25+%29%29%2Ax%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Added fractions or integers together <BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-highlight_green%28+5%2F100+%29%29%2Ax%2B0.6=0& border=1  ALIGN=MIDDLE  ALT=\"%28-highlight_green%28+5%2F100+%29%29%2Ax%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+%28-highlight_red%28+5%2F100+%29%29%2Ax+%29%2B0.6=0 ALIGN=MIDDLE  ALT=\"highlight_red%28+%28-highlight_red%28+5%2F100+%29%29%2Ax+%29%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Remove unneeded parentheses around factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+5+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+1%2F100+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+1%2F100+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-highlight_green%28+5+%29%2Fhighlight_green%28+100+%29%2Ax%2B0.6=0& border=1  ALIGN=MIDDLE  ALT=\"-highlight_green%28+5+%29%2Fhighlight_green%28+100+%29%2Ax%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-highlight_red%28+5+%29%2Fhighlight_red%28+100+%29%2Ax%2B0.6=0 ALIGN=MIDDLE  ALT=\"-highlight_red%28+5+%29%2Fhighlight_red%28+100+%29%2Ax%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Factors 5 and 100 have <A  rel=nofollow HREF=/algebra/homework/divisibility/>greatest common factor (GCF)</A> of 5. Reducing <A  rel=nofollow HREF=/algebra/homework/NumericFractions/>fraction</A>. <BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-highlight_green%28+1+%29%2Fhighlight_green%28+20+%29%2Ax%2B0.6=0& border=1  ALIGN=MIDDLE  ALT=\"-highlight_green%28+1+%29%2Fhighlight_green%28+20+%29%2Ax%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-highlight_red%28+1+%29%2F20%2Ax%2B0.6=0 ALIGN=MIDDLE  ALT=\"-highlight_red%28+1+%29%2F20%2Ax%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Remove extraneous '1' from product <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+1+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2F20%2B0.6=0& border=1  ALIGN=MIDDLE  ALT=\"-x%2F20%2B0.6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<HR width=50% align=left>Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+-x%2F20%2B0.6+%29=0 ALIGN=MIDDLE  ALT=\"highlight_red%28+-x%2F20%2B0.6+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR> Solved <A  rel=nofollow HREF=/algebra/homework/Linear-equations/>linear equation</A> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_red%28+-x%2F20%2B0.6=0+%29 ALIGN=MIDDLE  ALT=\"highlight_red%28+-x%2F20%2B0.6=0+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > equivalent to  -0.05*x+0.6  =0 <BR>It becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28+0+%29=0& border=1  ALIGN=MIDDLE  ALT=\"highlight_green%28+0+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR><B>Result</B>: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0& border=2 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<B>This is an <A  rel=nofollow HREF=/algebra/homework/equations/>equation</A>!</B> Solutions: <FONT SIZE=+2><U><B>x=12</B></U></FONT>.<BR><BR><H3  DISABLED_style= \"background-color: #88ccDD; font-weight: bold; margin-top: 0px; margin-bottom: 3px; text-align: center; padding: 2px;\">Universal Simplifier and Solver</H3>\n" );
document.write( "<BR>Done!<BR></TD></TR></TABLE><BR>\n" );
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document.write( "With x=12 then 32-x=20\r<BR>\n" );
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document.write( "Check the total dollar value  0.20*12 + 0.25*20 =2.40+5.00=7.40 which is a true statement.\r<BR>\n" );
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document.write( "Step 7.  ANSWER:  The number of 20-cent stamps is 12 and the number of 25-cent stamps is 20.\r<BR>\n" );
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document.write( "I hope the above steps and explanation were helpful.\r<BR>\n" );
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document.write( "For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.\r<BR>\n" );
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document.write( "And good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J\r<BR>\n" );
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document.write( "http://www.FreedomUniversity.TV<BR>\n" );
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