document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193333>Question 193333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please check my work and let me know if I have the right answers, thank you.<BR>\n" );
document.write( "Applications of Linear Equations <BR>\n" );
document.write( "1.	Joe has a collection of nickels and dimes that is worth $6.05. If the number of dimes was doubled and the number of nickels was decreased by 10, the value of the coins would be $9.85. How many dimes does he have?\r<BR>\n" );
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document.write( "43 dimes\r<BR>\n" );
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document.write( "x * $0.1 + y * $0.05 = $6.05\r<BR>\n" );
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document.write( "x * 2 * $0.1 + (y - 10) * $0.05 = $9.85\r<BR>\n" );
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document.write( "Solve for x in equation 1\r<BR>\n" );
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document.write( "x * $0.1 = $6.05 - y * $0.05\r<BR>\n" );
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document.write( "x = $60.5 - $0.5y\r<BR>\n" );
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document.write( "Plug into equation 2\r<BR>\n" );
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document.write( "($60.5 - $0.5y) * 2 * $0.1 + (y - 10) * $0.05 = $9.85\r<BR>\n" );
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document.write( "$12.1 - $0.1y + $0.05y - $0.5 = $9.85\r<BR>\n" );
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document.write( "$1.75 = $0.05y\r<BR>\n" );
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document.write( "y = 35 nickels\r<BR>\n" );
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document.write( "x * $0.1 + 35 * $0.05 = $6.05\r<BR>\n" );
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document.write( "$0.1x = $4.30\r<BR>\n" );
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document.write( "x = 43 dimes\r<BR>\n" );
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document.write( "Confirm result, does\r<BR>\n" );
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document.write( "43 * 2 * $0.1 + (35 - 10) * $0.05 = $9.85\r<BR>\n" );
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document.write( "$9.85 = $9.85\r<BR>\n" );
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document.write( "Yes\r<BR>\n" );
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document.write( "2.	An express train and a local train both leave Gray’s Lake at 12:00 noon and head for Chicago 60 miles away. The express travels twice as fast as the local and arrives 2 hours ahead of it.  Find the speed of each train. \r<BR>\n" );
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document.write( "v1 = speed of express train<BR>\n" );
document.write( "v2 = speed of local train\r<BR>\n" );
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document.write( "v1 = 30 MPH<BR>\n" );
document.write( "V2 = 15 MPH\r<BR>\n" );
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document.write( "v = d/t (velocity = distance / time)\r<BR>\n" );
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document.write( "t = d/v\r<BR>\n" );
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document.write( "t1 = 60 miles / 30 MPH\r<BR>\n" );
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document.write( "t1 = 2 hours\r<BR>\n" );
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document.write( "t2 = 60 miles / 15 MPH\r<BR>\n" );
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document.write( "t2 = 4 hours\r<BR>\n" );
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document.write( "Does, t1 = t2 - 2\r<BR>\n" );
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document.write( "2 hours = 2 hours\r<BR>\n" );
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document.write( "Yes\r<BR>\n" );
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document.write( "3.	Walt made an extra $12,000 last year from a part-time job. He invested part of the money at 7% and the rest at 9%. He made a total of $970 in interest. How much was invested at 7%?<BR>\n" );
document.write( "$5500 invested at 7%\r<BR>\n" );
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document.write( "x + y = $12,000<BR>\n" );
document.write( "x * 0.07 + y * 0.09 = $970\r<BR>\n" );
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document.write( "x = $12,000 - y\r<BR>\n" );
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document.write( "($12,000 - y) * 0.07 + y * 0.09 = $970\r<BR>\n" );
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document.write( "$840 - 0.07y + 0.09y = $970\r<BR>\n" );
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document.write( "0.02y = $130\r<BR>\n" );
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document.write( "y = $6500 @ 9%, which means x = $5500 @ 7%\r<BR>\n" );
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document.write( "Double check, does\r<BR>\n" );
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document.write( "$5500 * 0.07 + $6500 * 0.09 = $970\r<BR>\n" );
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document.write( "$970 = $970\r<BR>\n" );
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document.write( "Yes </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145151 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=145151\">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( "#1 and #3 are done correctly.  You have the correct answers for #2, but you really don't show how you got them.\r<BR>\n" );
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document.write( "Express train:\r<BR>\n" );
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document.write( "Local train:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d = v_2(t + 2)\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "Since the distances are the same:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2v_2t - v_2t = 2v_2\">\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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