document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205238>Question 205238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Martin purchases 2 apples and 4 oranges. Michelle purchases 8 apples and 2 oranges. If Michelle pays twice as much as Martin. How many apples can be purchased for the price of 9 oranges?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154919 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let cost of apples = x<BR>\n" );
document.write( "let cost of oranges = y<BR>\n" );
document.write( "let b = how much martin pays<BR>\n" );
document.write( "let g = how much michelle pays<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b = 2x + 4y<BR>\n" );
document.write( "g = 8x + 2y<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the assumption is that they both pay the same price per apple and the same price per orange.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "michelle pays twice as much as martin so:<BR>\n" );
document.write( "g = 2*b<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if g = 2*b then:<BR>\n" );
document.write( "8x +2y = 2*(2x + 4y)<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "8x + 2y = 4x + 8y<BR>\n" );
document.write( "subtract 4x from both sides of the equation and subtract 2y from both sides of the equation to get:<BR>\n" );
document.write( "8x - 4x = 8y - 2y<BR>\n" );
document.write( "which results in:<BR>\n" );
document.write( "4x = 6y<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the question is:<BR>\n" );
document.write( "how many apples can be purchased for the price of 9 oranges.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "To find that you need to find the price of oranges in comparison to the price of apples.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Since y is the price of oranges, then solve for y in the equation of:<BR>\n" );
document.write( "4x = 6y<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Dividing both sides of this equation by 6 gets:<BR>\n" );
document.write( "Y = 4x/6 = (2/3)*x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The price of 9 oranges would then be 9 * y = 9 * (2/3)*x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "This results in (18/3) * x<BR>\n" );
document.write( "Which reduces to:<BR>\n" );
document.write( "6*x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The price of 9 oranges is 6 apples.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "One way to check your answer is to place this results in the original equations and see what comes out.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The original cost to Martin was:<BR>\n" );
document.write( "2x + 4y<BR>\n" );
document.write( "since y = (2/3)*x then this cost becomes:<BR>\n" );
document.write( "2x + 4*(2/3)*x which becomes:<BR>\n" );
document.write( "2x + (8/3)*x which becomes:<BR>\n" );
document.write( "(14/3)*x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the original cost to Michelle was:\"<BR>\n" );
document.write( "8x + 2y<BR>\n" );
document.write( "since y = (2/3)*x then this cost becomes:<BR>\n" );
document.write( "8x + (2*(2/3)*x which becomes:<BR>\n" );
document.write( "8x + (4/3)*x which becomes:<BR>\n" );
document.write( "(28/3)*x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since michelle paid twice as much as martin, and:<BR>\n" );
document.write( "(28/3)*x is 2 times (14/3)*x, then the equation looks good and you can say with reasonable confidence that the price of 9 oranges is 6 apples.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );