document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204793>Question 1204793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Annie has a piggy bank consisting of quarters dimes and nickels. She has a total 74 coins in the bank totaling 11.35$. There are half as many dimes as quarters. How many nickels does Annie have? </SPAN>\n" );
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document.write( "\"There are half as many dimes as quarters\" which flips around to \"There are twice as many quarters as dimes\".\r<BR>\n" );
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document.write( "# of quarters = 2*(# of dimes)\r<BR>\n" );
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document.write( "Let x = number of dimes<BR>\n" );
document.write( "2x = number of quarters<BR>\n" );
document.write( "x+2x = 3x = number of dimes and quarters\r<BR>\n" );
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document.write( "Annie has 74 coins total. <BR>\n" );
document.write( "3x of them are either quarters or dimes, so the remaining 74-3x coins must be nickels.\r<BR>\n" );
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document.write( "x = number of dimes<BR>\n" );
document.write( "10x = value of the dimes in cents<BR>\n" );
document.write( "2x = number of quarters<BR>\n" );
document.write( "25*2x = 50x = value of the quarters in cents<BR>\n" );
document.write( "74-3x = number of nickels<BR>\n" );
document.write( "5*(74-3x) = 370 - 15x = value of the nickels in cents\r<BR>\n" );
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document.write( "total value in cents = 10x+50x+370-15x = 45x+370\r<BR>\n" );
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document.write( "Set this equal to the total amount Annie has which is 1135 cents (aka $11.35)\r<BR>\n" );
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document.write( "45x+370 = 1135<BR>\n" );
document.write( "45x = 1135-370<BR>\n" );
document.write( "45x = 765<BR>\n" );
document.write( "x = 765/45<BR>\n" );
document.write( "x = 17\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "number of dimes = x = 17<BR>\n" );
document.write( "number of quarters = 2x = 2*17 = 34<BR>\n" );
document.write( "number of nickels = 74-3x = 74-3*17 = <font color=red>23</font>\r<BR>\n" );
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document.write( "In short,<BR>\n" );
document.write( "number of dimes = 17<BR>\n" );
document.write( "number of quarters = 34<BR>\n" );
document.write( "number of nickels = <font color=red>23</font>\r<BR>\n" );
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document.write( "Check<BR>\n" );
document.write( "17 dimes + 34 quarters + 23 nickels = 17*10 + 34*25 + 23*5 = 1135 cents = $11.35<BR>\n" );
document.write( "This helps confirm the answer.<BR>\n" );
document.write( "Further confirmation comes from the fact that 17+34+23 = 74\r<BR>\n" );
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document.write( "Answer: She has <font color=red size=4>23 nickels</font><BR>\n" );
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