document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=221298>Question 221298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A coin operated washing machine contains $19.95 in nickels and quarters. If there is one less nickel than 3 times the number of quarters, how many of each are there?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #166018 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=166018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A coin operated washing machine contains $19.95 in nickels and quarters. If there is one less nickel than 3 times the number of quarters, how many of each are there? \r<BR>\n" );
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document.write( "Step 1.  Let x be the number of nickels.\r<BR>\n" );
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document.write( "Step 2.  Let 0.05x be the dollar value of nickels.\r<BR>\n" );
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document.write( "Step 3.  Let y be the number of quarters.\r<BR>\n" );
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document.write( "Step 4.  Let 0.25y be the dollar value of quarters.\r<BR>\n" );
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document.write( "Step 5.  0.05x+0.25y=19.95 or 5x+25y=1995since coin operated washing machine contains $19.95 in nickels and quarters.\r<BR>\n" );
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document.write( "Step 6.  x+1=3y or x-3y=-1 since there is one less nickel than 3 times the number of quarters\r<BR>\n" );
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document.write( "Step 7.  We have linear system of equations in Steps 5 and 6.\r<BR>\n" );
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document.write( "5x+25y=1995<BR>\n" );
document.write( "x-3y=-1\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=linear_substitution.solver>SOLVE linear system by SUBSTITUTION</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++5%5Cx+%2B+25%5Cy+=+1995%2C%0D%0A++++1%5Cx+%2B+-3%5Cy+=+-1+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++5%5Cx+%2B+25%5Cy+=+1995%2C%0D%0A++++1%5Cx+%2B+-3%5Cy+=+-1+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 25*y to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ax+=+1995+-+25%2Ay ALIGN=MIDDLE  ALT=\"5%2Ax+=+1995+-+25%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1995%2F5+-+25%2Ay%2F5 ALIGN=MIDDLE  ALT=\"x+=+1995%2F5+-+25%2Ay%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute that<BR>\n" );
document.write( "  into another equation:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2A%281995%2F5+-+25%2Ay%2F5%29+%2B+-3%5Cy+=+-1 ALIGN=MIDDLE  ALT=\"1%2A%281995%2F5+-+25%2Ay%2F5%29+%2B+-3%5Cy+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that y=50. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1995%2F5+-+25%2Ay%2F5 ALIGN=MIDDLE  ALT=\"x+=+1995%2F5+-+25%2Ay%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, x=149.<BR>\n" );
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document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x=149%2C+y=50+%29 ALIGN=MIDDLE  ALT=\"system%28+x=149%2C+y=50+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "x=149 and y=50\r<BR>\n" );
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document.write( "Check dollar value:  149*0.05+50*0.25=7.45+12.50=19.95 and there is one less nickel (149) than 3 times the number of quarters (3*50=150)...both are true statements.\r<BR>\n" );
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document.write( "Step 8.  ANSWER:  There are 149 nickels and 50 quarters.\r<BR>\n" );
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document.write( "I hope the above steps 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( "Good luck in your studies!\r<BR>\n" );
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document.write( "Respectfully,<BR>\n" );
document.write( "Dr J<BR>\n" );
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