document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177083>Question 1177083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> “A purse contains $11.65 in quarters (25 cents) and dimes(10cents). If the total number of<BR>\n" );
document.write( "coins is 70, find how many quarters and dimes are there.” </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #805311 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=805311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) An algebraic setup using two variables....<br><BR>\n" );
document.write( "Let d = # of dimes<BR>\n" );
document.write( "Let q = # of quarters<br><BR>\n" );
document.write( "d+q=70  (the total number of coins is 70)<BR>\n" );
document.write( "10d+25q = 1165  (the total value of the coins -- 10 cents for each dime and 25 cents for each quarter -- is $11.65, or 1165 cents)<br><BR>\n" );
document.write( "Solve using either substitution or elimination....<br><BR>\n" );
document.write( "(2) An algebraic setup using a single variable....<br><BR>\n" );
document.write( "Let d = # of dimes<BR>\n" );
document.write( "Then 70-d = # of quarters  (because the total number of coins is 70)<br><BR>\n" );
document.write( "The total value of the coins is $11.65:<br><BR>\n" );
document.write( "10(d)+25(70-d) = 1165<br><BR>\n" );
document.write( "Solve using basic algebra.<br><BR>\n" );
document.write( "(3) a quick mental solution, if formal algebra is not required, and/or if getting the answer quickly is advantageous....<br><BR>\n" );
document.write( "If all 70 coins were dimes, the value would be 700 cents; the actual value is 465 cents more than that.<BR>\n" );
document.write( "Exchanging a dime for a quarter keeps the number of coins at 70 but increases the total value by 25-10 = 15 cents.<BR>\n" );
document.write( "The number of times a dime needs to be exchanged for a quarter to make up the addition 465 cents is 465/15 = 31.<BR>\n" );
document.write( "So there must be 31 quarters, which means 70-31 = 39 dimes.<br><BR>\n" );
document.write( "ANSWER: 31 quarters and 39 dimes.<br><BR>\n" );
document.write( "CHECK: 31(25)+39(10) = 775+390 = 1165<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );