document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202342>Question 1202342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Micky and Yarberry saved nickels and dimes. They had a total of 34 coins whose value was $2.70. How many of each kind did they have? </SPAN>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "<font color=red>14 nickels, 20 dimes</font>\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "Method 1\r<BR>\n" );
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document.write( "n = number of nickels<BR>\n" );
document.write( "34-n = number of dimes\r<BR>\n" );
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document.write( "5n = value of the nickels (cents)<BR>\n" );
document.write( "10(34-n) = 340-10n = value of the dimes (cents)<BR>\n" );
document.write( "5n+340-10n = -5n+340 = total value (cents)\r<BR>\n" );
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document.write( "$2.70 = 2.70*100 = 270 cents\r<BR>\n" );
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document.write( "-5n+340 = 270<BR>\n" );
document.write( "-5n = 270-340<BR>\n" );
document.write( "-5n = -70<BR>\n" );
document.write( "n = -70/(-5)<BR>\n" );
document.write( "n = 14<BR>\n" );
document.write( "They have <font color=red>14 nickels</font>\r<BR>\n" );
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document.write( "And also<BR>\n" );
document.write( "34-n = 34-14 = <font color=red>20 dimes</font>\r<BR>\n" );
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document.write( "Method 2\r<BR>\n" );
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document.write( "Let's say we start with all 34 coins as nickels<BR>\n" );
document.write( "34 nickels = 34*5 = 170 cents\r<BR>\n" );
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document.write( "The gap from 170 cents to the target goal of 270 cents is 270-170 = 100 cents.<BR>\n" );
document.write( "To get to the target, we'll need to replace some nickels with dimes.\r<BR>\n" );
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document.write( "Each time we replace a nickel with a dime, the net value increase is 5 cents (because 10 cents - 5 cents = 5 cents)\r<BR>\n" );
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document.write( "Let x be the number of times we replace a nickel with a dime.<BR>\n" );
document.write( "5x then represents the total net increase. We want this to equal the 100 cents calculated earlier.\r<BR>\n" );
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document.write( "5x = 100<BR>\n" );
document.write( "x = 100/5<BR>\n" );
document.write( "x = 20<BR>\n" );
document.write( "We must replace 20 nickels with 20 dimes\r<BR>\n" );
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document.write( "34 nickels drops to 34-20 = <font color=red>14 nickels</font><BR>\n" );
document.write( "0 dimes increases to 0+20 = <font color=red>20 dimes</font>\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "14 nickels + 20 dimes = 34 coins total<BR>\n" );
document.write( "That validates the coin count requirement.\r<BR>\n" );
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document.write( "A = 14 nickels = 14*5 = 70 cents<BR>\n" );
document.write( "B = 20 dimes = 20*10 = 200 cents<BR>\n" );
document.write( "A+B = 70 cents + 200 cents = 270 cents = $2.70<BR>\n" );
document.write( "That validates the total value requirement.\r<BR>\n" );
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document.write( "Both conditions have been met. The answers are confirmed.<BR>\n" );
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