document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141370>Question 1141370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> she has 1.10, she has three times as many 5-cents coins as 1 cent coins, and the number of 10 cents coins is two less than the number of 1 cent coins. how many 10 cents coins, 5 cents coins, and 1 cent coins does she have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #761915 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=761915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The information is given in such a way that the numbers of 5-cent and 10-cent coins are both defined in terms of the number of 1-cent coins.  So choosing x to represent the number of 1-cent coins should make the problem easiest.<br><BR>\n" );
document.write( "Let x = # of 1-cent coins<BR>\n" );
document.write( "Then 3x = # of 5-cent coins<BR>\n" );
document.write( "And x-2 = # of 10-cent coins<br><BR>\n" );
document.write( "Now write and solve the equation that says the total value is $1.10, or 110 cents:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%28x-2%29%2B5%283x%29%2B1%28x%29+=+110 ALIGN=MIDDLE  ALT=\"10%28x-2%29%2B5%283x%29%2B1%28x%29+=+110\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You can finish solving the problem from there....<br><BR>\n" );
document.write( "-------------------------------------------------<br><BR>\n" );
document.write( "You can also solve the problem informally using logical reasoning.<br><BR>\n" );
document.write( "(1) The total value of all the coins (110) is a multiple of 5; and the total value of all the 5- and 10-cent coins is a multiple of 5.  That means the total value of the 1-cent coins must be a multiple of 5 -- i.e., the number of 1-cent coins is a multiple of 5.<br><BR>\n" );
document.write( "(2) So the number of 1-cent coins is 5, or 10, or 15, ....<br><BR>\n" );
document.write( "(3) But the number of 5-cent coins is 3 times the number of 1-cent coins.  If the number of 1-cent coins were 10, the number of 5-cent coins would be 30; and 30 5-cent coins is more than the actual total value of all the coins.<br><BR>\n" );
document.write( "(4) So the number of 1-cent coins HAS TO BE 5.  Then the number of 5-cent coins is 3*5 = 15, and the number of 10-cent coins is 5-2 = 3.<br><BR>\n" );
document.write( "CHECK: 3(10)+15(5)+5(1) = 30+75+5 = 110<br><BR>\n" );
document.write( "-------------------------------------------------------<br><BR>\n" );
document.write( "Knowing how to solve problems like this using formal algebra is of course useful... but it is excellent brain exercise to be able to solve them using logical reasoning. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );