document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249989>Question 249989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An apple costs the same as 2oranges. Together, an orange and a banana cost .10 more than an apple. Two oranges cost .15 more than a banana. what is the cost for one of each fruit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181993 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=181993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A = cost of an apple<BR>\n" );
document.write( "O = cost of an orange<BR>\n" );
document.write( "B = cost of a banana<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The apple costs the same as 2 oranges...<BR>\n" );
document.write( "A = 2*O<BR>\n" );
document.write( "or<BR>\n" );
document.write( "O = A/2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "An orange and a banana costs 10 cents more than an apple...<BR>\n" );
document.write( "A + 10 = O + B<BR>\n" );
document.write( "so<BR>\n" );
document.write( "A = O + B - 10<BR>\n" );
document.write( "and<BR>\n" );
document.write( "O = A + 10 - B<BR>\n" );
document.write( "and<BR>\n" );
document.write( "B = A + 10 - O<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Two oranges cost 15 cents more than a banana<BR>\n" );
document.write( "2*O = B + 15<BR>\n" );
document.write( "so<BR>\n" );
document.write( "O = (B+15)/2<BR>\n" );
document.write( "and<BR>\n" );
document.write( "B = 2*O - 15<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now we solve these equations.<BR>\n" );
document.write( "The key strategy is to get all of the costs in terms of the same fruit...<BR>\n" );
document.write( "Since we have 3 equations that can be defined in terms of O, we can start with that.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "O = A/2<BR>\n" );
document.write( "O = A + 10 - B<BR>\n" );
document.write( "O = (B+15)/2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If a=b and b=c, then a=c.  So we know:<BR>\n" );
document.write( "A/2 = A+10 - B<BR>\n" );
document.write( "A = 2A + 20 - 2B<BR>\n" );
document.write( "2B = A + 20<BR>\n" );
document.write( ". <BR>\n" );
document.write( "A/2 = (B+15)/2<BR>\n" );
document.write( "A = B+15<BR>\n" );
document.write( "B = A - 15<BR>\n" );
document.write( "2B = 2A - 30<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A+20 = 2A - 30<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A = 50<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using A = 50 cents, we are able to find the other values by substituting back into the original equations.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "A = 2*O<BR>\n" );
document.write( "so<BR>\n" );
document.write( "O = 25<BR>\n" );
document.write( ".<BR>\n" );
document.write( "B = A + 10 - O<BR>\n" );
document.write( "B = 50 + 10 - 25<BR>\n" );
document.write( "B = 35<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substituting back into the initial equations, we are able to check these values.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The apple costs the same as 2 oranges...<BR>\n" );
document.write( "This statement was used to calculate the value of the oranges, so of course it checks.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "An orange and a banana costs 10 cents more than an apple...<BR>\n" );
document.write( "O + B = 25 + 35 = 60<BR>\n" );
document.write( "That is 10 cents more than an apple, so it checks.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Two oranges cost 15 cents more than a banana<BR>\n" );
document.write( "2*25 = 50, which is 15 cents more than a banaa.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "These all check.<BR>\n" );
document.write( "So we can conclude that in this case:<BR>\n" );
document.write( "Apples cost 50 cents.<BR>\n" );
document.write( "Oranges cost 25 cents.<BR>\n" );
document.write( "Bananas cost 35 cents.<BR>\n" );
document.write( ",<BR>\n" );
document.write( "Done </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );