document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149203>Question 149203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am supposed to set these up as an equation and solve I thought I had it but my answers look incorrect could you do it so that I can see what I did wrong? Thank you so much.\r<BR>\n" );
document.write( "\n" );
document.write( "Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have? \r<BR>\n" );
document.write( "\n" );
document.write( "and \r<BR>\n" );
document.write( "\n" );
document.write( "Walt made an extra $9000 last year from a part-time job. He invested part of the money at 9% and the rest at 8%. He made a total of $770 in interest. How much was invested at 8%? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109459 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have? <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let n = number of nickels<BR>\n" );
document.write( "and d = number of dimes<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Because we have two unknowns we need two equations:<BR>\n" );
document.write( "From: \"Joe has a collection of nickels and dimes that is worth $5.65.\" we get<BR>\n" );
document.write( ".05n + .10d = 5.65 (equation 1)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "From: \"If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45.\" we get:<BR>\n" );
document.write( ".05(n+8) + .10(2d) = 10.45<BR>\n" );
document.write( ".05n + .40 + .20d = 10.45<BR>\n" );
document.write( ".05n + .20d = 10.05 (equation 2)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "n = 25 (nickels)<BR>\n" );
document.write( "d = 44 (dimes)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Below shows the details:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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++++0.05%5Cn+%2B+0.1%5Cd+=+5.65%2C%0D%0A++++0.05%5Cn+%2B+0.2%5Cd+=+10.05+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >We'll use substitution. After moving 0.1*d to the right, we get:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.05%2An+=+5.65+-+0.1%2Ad ALIGN=MIDDLE  ALT=\"0.05%2An+=+5.65+-+0.1%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+5.65%2F0.05+-+0.1%2Ad%2F0.05 ALIGN=MIDDLE  ALT=\"n+=+5.65%2F0.05+-+0.1%2Ad%2F0.05\"   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=0.05%2A%285.65%2F0.05+-+0.1%2Ad%2F0.05%29+%2B+0.2%5Cd+=+10.05 ALIGN=MIDDLE  ALT=\"0.05%2A%285.65%2F0.05+-+0.1%2Ad%2F0.05%29+%2B+0.2%5Cd+=+10.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > and simplify: So, we know that d=44. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+5.65%2F0.05+-+0.1%2Ad%2F0.05 ALIGN=MIDDLE  ALT=\"n+=+5.65%2F0.05+-+0.1%2Ad%2F0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" >, n=25.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+n=25%2C+d=44+%29 ALIGN=MIDDLE  ALT=\"system%28+n=25%2C+d=44+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( "***************************************<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Walt made an extra $9000 last year from a part-time job. He invested part of the money at 9% and the rest at 8%. He made a total of $770 in interest. How much was invested at 8%?<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let x = amount invested at 9%<BR>\n" );
document.write( "9000-x = amount invested at 8%<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".09x + .08(9000-x) = 770<BR>\n" );
document.write( ".09x + 720 - .08x = 770<BR>\n" );
document.write( ".09x - .08x = 50<BR>\n" );
document.write( ".01x = 50<BR>\n" );
document.write( "x = $5000 (invested at 9%)<BR>\n" );
document.write( "9000-5000 = $4000 (invested at 8%)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );