document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181298>Question 1181298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> plan international offers gifts of hope options where you select a gift to support a community in a developing country. it costs 500 euros to equip a school room and 295 euros to send a girl to school. If you buy 20 gifts at a total cost of 6515 euros, how many classrooms will be equipped and how many girls will be sent to school. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #811296 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=811296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A total of 20 gifts that cost either 295 or 500 euros each are being bought, and a total of 6515 euros is being spent.  You need to determine how many of each are being bought.<br><BR>\n" );
document.write( "For a student just learning basic algebra, I see three basic ways to set up this problem for solving.<br><BR>\n" );
document.write( "(1) Using two equations and elimination<br><BR>\n" );
document.write( "let x = # of gifts at 295 euros each<BR>\n" );
document.write( "let y = # of gifts at 500 euros each<br><BR>\n" );
document.write( "x+y=20<BR>\n" );
document.write( "295x+500y=6515<br><BR>\n" );
document.write( "With two equations in this form, usually solving by elimination is easiest.<br><BR>\n" );
document.write( "(2) Using two equations and substitution.<br><BR>\n" );
document.write( "You can start the same way as in (1), but instead of using elimination, solve the first equation to get y=20-x and substitute that into the second equation.<br><BR>\n" );
document.write( "(3) Using a single equation<br><BR>\n" );
document.write( "let x = # of gifts at 295 euros each<BR>\n" );
document.write( "then 20-x = # of gifts at 500 euros each<br><BR>\n" );
document.write( "Then you only need to solve a single equation to find the answer:<br><BR>\n" );
document.write( "295(x)+500(20-x)=6515<br><BR>\n" );
document.write( "I personally would never use method (2) above, because it is exactly like method (3) but with an extra step.  For me, methods (1) and (3) are equally good.<br><BR>\n" );
document.write( "Try the different methods and find one that \"works\" best for you.<br><BR>\n" );
document.write( "And here is my personal favorite for a fast way to solve this kind of problem, if a formal algebraic solution is not required.<br><BR>\n" );
document.write( "20 gifts all at 295 euros each would cost 5900 euros; the actual total is 6515 euros, which is another 615 euros.<BR>\n" );
document.write( "The difference in the cost between the two gifts is 500-295=205 euros.<BR>\n" );
document.write( "To make the needed additional 615 euros, the number of higher priced gifts must be 615/205=3.<br><BR>\n" );
document.write( "ANSWER: 3 gifts at 500 euros each; 17 at 295 euros each.<br><BR>\n" );
document.write( "CHECK: 500(3)+295(17) = 1500+5015 = 6515<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );