document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082722>Question 1082722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> systems of equations: Larry has $4 in nickels and quarters. If there are 36 coins in all, how many nickels and how many quarters does Larry have. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696792 by </B><A HREF=/tutors/aboutme.mpl?userid=My+Virtual+Math+Guide><B>My Virtual Math Guide(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=My+Virtual+Math+Guide><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=My+Virtual+Math+Guide><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=696792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's define variables. Let n = number of nickels, and q = number of quarters. If Larry has $4 in nickels and quarters, then our first equation is\r<BR>\n" );
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document.write( "0.05n + 0.25q = 4 (since a nickel is 5 cents, and a quarter is 25 cents)\r<BR>\n" );
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document.write( "Since there are 36 coins, then n + q = 36\r<BR>\n" );
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document.write( "Now, we have to solve the equation simultaneously. We can use the substitution method. We can rewrite the second equation as n = 36 - q, then substitute into the first equation to get:\r<BR>\n" );
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document.write( "0.05(36 - q) + 0.25q = 4\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "1.8 - 0.05q + 0.25q = 4\r<BR>\n" );
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document.write( "Simplify further:\r<BR>\n" );
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document.write( "1.8 + 0.2q = 4\r<BR>\n" );
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document.write( "To find q, first subtract 1.8 from both sides of the equation to get:\r<BR>\n" );
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document.write( "0.2q = 4 - 1.8 = 2.2\r<BR>\n" );
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document.write( "Now, divide both sides by 0.2 to get:\r<BR>\n" );
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document.write( "q = 2.2/0.2 = 11\r<BR>\n" );
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document.write( "To solve for n, remember n + q = 36\r<BR>\n" );
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document.write( "So n + 11 = 36<BR>\n" );
document.write( "subtract 11 from both sides of the equation:<BR>\n" );
document.write( "n = 36 - 11 = 25\r<BR>\n" );
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document.write( "Now that we have the values of n and q, we can check our answers to make sure we are right.\r<BR>\n" );
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document.write( "Equation 1: 0.05n + 0.25q = 4\r<BR>\n" );
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document.write( "Let's substitute the values of n and q into the equation to see if it makes the equation true.\r<BR>\n" );
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document.write( "0.05(25) + 0.25(11) = 1.25 + 2.75 = 4\r<BR>\n" );
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document.write( "Our answer is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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