document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=230553>Question 230553</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carlos has some pennies, nickels, and quarters in his pocket. He has 2 more nickels than quarters. He has twice as many pennies as nickels. The total value is $1.74. How many of each coin does Carlos have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #170713 by </B><A HREF=/tutors/aboutme.mpl?userid=likaaka><B>likaaka(51)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=likaaka><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=170713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First begin by naming your variables.<BR>\n" );
document.write( "Let P be the amount, not worth, of pennies Carlos has, N will be the amount of nickels, and Q the amount of quarters.<BR>\n" );
document.write( "So if Carlos has 2 more nickels than quarters, your first equation is<BR>\n" );
document.write( "N = Q + 2<BR>\n" );
document.write( "If he has twice as many pennies as nickels, then<BR>\n" );
document.write( "P = 2N<BR>\n" );
document.write( "Now we use the value of each coin to determine the third equation.<BR>\n" );
document.write( "0.01P + 0.05N + 0.25Q = 1.74\r<BR>\n" );
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document.write( "Here's your system of equations<BR>\n" );
document.write( "N = Q + 2<BR>\n" );
document.write( "P = 2N<BR>\n" );
document.write( "0.01P + 0.05N + 0.25Q = 1.74<BR>\n" );
document.write( "I would start be rearranging the first equation so that it's solved for Q<BR>\n" );
document.write( "N = Q + 2 becomes Q = N - 2 by subtracting 2 from both sides\r<BR>\n" );
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document.write( "Now substitute the value of Q and the value of P into the third equation to solve for N<BR>\n" );
document.write( "0.01(2N) + 0.05N + 0.25(N-2) = 1.74, distribute <BR>\n" );
document.write( "0.02N + 0.05N + 0.25N - 0.5 = 1.74, combine like terms<BR>\n" );
document.write( "0.32N - 0.5 = 1.74, add 0.5 to both sides<BR>\n" );
document.write( "0.32N = 2.24, divide both sides by 0.32<BR>\n" );
document.write( "N = 7, so Carlos has 7 nickels\r<BR>\n" );
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document.write( "Given Q = N - 2 and N = 7 solve for Q<BR>\n" );
document.write( "Q = 7 - 2<BR>\n" );
document.write( "Q = 5, so Carlos has 5 quarters\r<BR>\n" );
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document.write( "Given P = 2N and N = 7<BR>\n" );
document.write( "P = 2(7)<BR>\n" );
document.write( "P = 14, so Carlos has 14 pennies\r<BR>\n" );
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document.write( "CHECK: <BR>\n" );
document.write( "0.01(14) + 0.05(7) + 0.25(5) = 1.74<BR>\n" );
document.write( "0.14 + 0.35 + 1.25 = 1.74<BR>\n" );
document.write( "1.74 = 1.74<BR>\n" );
document.write( " </SPAN>\n" );
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