document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969658>Question 969658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man has 20 coins in his pocket consisting of 5 peso, 10 peso and 1 peso coins. There are an equal equation of ones and fives among them. He has 88 pesos in all. How many coins of each denomination are there? </SPAN>\n" );
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document.write( "A solution using three variables for the numbers of 1-, 5-, and 10-peso coins is good algebra; with three variables you will need three equations.  But setting up the problem using a single variable will make solving the problem easier, since there will be only one equation.<br><BR>\n" );
document.write( "x = number of 1-peso coins<BR>\n" );
document.write( "x = number of 5-peso coins<BR>\n" );
document.write( "20-2x = number of 10-peso coins<br><BR>\n" );
document.write( "The total value is 88 pesos:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%28x%29%2B5%28x%29%2B10%2820-2x%29=88 ALIGN=MIDDLE  ALT=\"1%28x%29%2B5%28x%29%2B10%2820-2x%29=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B200-20x=88 ALIGN=MIDDLE  ALT=\"6x%2B200-20x=88\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x=112 ALIGN=MIDDLE  ALT=\"14x=112\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+112%2F14+=+8 ALIGN=MIDDLE  ALT=\"x+=+112%2F14+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 8 each 1-peso and 5-peso coins; 20-16=4 10-peso coins<br><BR>\n" );
document.write( "If a formal algebraic solution is not required, a quick solution can be obtained using logical reasoning and some simple mental arithmetic.<br><BR>\n" );
document.write( "Since the numbers of 1- and 5-peso coins are the same, consider them as groups of 2 coins with a value of 6 pesos.<br><BR>\n" );
document.write( "The total value of the 10-peso coins is a multiple of 10; since the total value of all the coins is 88 pesos, the total value of the 1- and 5-peso coins must have units digit 8.<br><BR>\n" );
document.write( "To get a units digit of 8, the number of 6-peso pairs of coins can be either 3 or 8. (3*6=18; 8*6=48).<br><BR>\n" );
document.write( "3 each of 1- and 5-peso coins worth a total of 18 pesos means 7 10-peso coins to make the other 70 pesos; 3+3+7=13 is not the right total number of coins.<br><BR>\n" );
document.write( "8 each of the 1- and 5-peso coins worth a total of 48 pesos means 4 10-peso coins to make the other 40 pesos; 8+8+4=20 is the right total number of coins.<br><BR>\n" );
document.write( "ANSWER: 8 each 1- and 5-peso coins; 4 10-peso coins.<br><BR>\n" );
document.write( " </SPAN>\n" );
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