document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935828>Question 935828</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The land of Jabral has two coins, the Jabr and the Al. <BR>\n" );
document.write( "Kirsten buys a typewriter with two Jabrs and gets an Al<BR>\n" );
document.write( "in change. Meanwhile, with one Jabr and two Als, her<BR>\n" );
document.write( "friend Sophia buys two of the same typewriters Kirsten<BR>\n" );
document.write( "purchased. How many of these typewriters could be<BR>\n" );
document.write( "purchased with ten Jabrs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569411 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=569411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x represent the value of 1 jabr.<BR>\n" );
document.write( "let y represent the value of 1 al.\r<BR>\n" );
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document.write( "cost of 1 typewriter = 2x - y<BR>\n" );
document.write( "cost of 2 typewriter = 1x + 2y\r<BR>\n" );
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document.write( "you get 2 equations.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "2x - y = 1<BR>\n" );
document.write( "1x + 2y = 2\r<BR>\n" );
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document.write( "these equations mean:\r<BR>\n" );
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document.write( "2 * the value of one jabr minus 1 * the value of one al = 1 * the cost of one typewriter\r<BR>\n" );
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document.write( "1 * the value of one jabr plus 2 * the value of 1 al = 2 * the cost of one typewriter.\r<BR>\n" );
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document.write( "in the first equation, solve for y to get:\r<BR>\n" );
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document.write( "2x - y = 1 becomes y = 2x - 1\r<BR>\n" );
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document.write( "in the second equation, replace y with 2x - 1 to get:\r<BR>\n" );
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document.write( "1x + 2y = 2 becomes 1x + 2(2x - 1) = 2 which becomes 1x + 4x - 2 = 2 which becomes 5x - 2 = 2.\r<BR>\n" );
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document.write( "add 2 to both sides of this equation to get:\r<BR>\n" );
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document.write( "5x = 4\r<BR>\n" );
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document.write( "divide both sides of this equation by 5 to get:\r<BR>\n" );
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document.write( "x = 4/5\r<BR>\n" );
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document.write( "this means that the value of 1 jabr is equal to 4/5 * the cost of 1 typewriter.\r<BR>\n" );
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document.write( "in the first original equation, replace x with 4/5 to get:\r<BR>\n" );
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document.write( "2x - y = 1 becomes 8/5 - y = 1\r<BR>\n" );
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document.write( "add y to both sides of this equation and subtract 1 from both sides of this equation to get:\r<BR>\n" );
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document.write( "8/5 - 1 = y which becomes 8/5 - 5/5 = y which becomes 3/5 = y\r<BR>\n" );
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document.write( "this means that the value of 1 al is equal to 3/5 * the cost of 1 typewriter.\r<BR>\n" );
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document.write( "you now know that:\r<BR>\n" );
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document.write( "x = 4/5 * the cost of 1 typewriter.<BR>\n" );
document.write( "y = 3/5 * the cost of 1 typewriter.\r<BR>\n" );
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document.write( "go back to your original equations to see if this is true.\r<BR>\n" );
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document.write( "first equation is 2x - y = 1 which becomes 2 * 4/5 - 3/5 = 1 which becomes 8/5 - 3/5 = 1 which becomes 5/5 = 1 which becomes 1 = 1 which his true.\r<BR>\n" );
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document.write( "second equation is 1x + 2y = 2 which becomes 4/5 + 2 * 3/5 = 2 which becomes 4/5 + 6/5 = 2 which becomes 10/5 = 2 which becomes 2 = 2 which is true.\r<BR>\n" );
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document.write( "the values of x and y are confirmed to be true.\r<BR>\n" );
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document.write( "you want to know how many typewriters you can buy with 10 jabr.\r<BR>\n" );
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document.write( "since x represents the value of one jabr and x is equal to 4/5, this means that 1 jabr is equivalent to 4/5 of the cost of 1 typewriter.\r<BR>\n" );
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document.write( "10 jabr = 10 * the value of 1 jabr = 10 * 4/5 = 40/5 = 8.\r<BR>\n" );
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document.write( "this means that 10 * the cost of 1 jabr = 8 times the cost of 1 typewriter.\r<BR>\n" );
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document.write( "this means you can buy 8 typewriters with 10 jabr.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "read on for a further explanation if you like, but you don't need to if you're happy with the solution as it stands.\r<BR>\n" );
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document.write( "if we put this in terms of dollars, it might make more sense.\r<BR>\n" );
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document.write( "let's assume that 1 jabr is equal to 100 dollars.\r<BR>\n" );
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document.write( "if we can buy 8 typewriters with 10 jabr, and 1 jabr = 100 dollars, then the cost of 8 typewriters is equal to 10 * 100 = 1000 dollars.\r<BR>\n" );
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document.write( "the cost per typewriter is therefore equal to 1000 / 8 = 125 dollars.\r<BR>\n" );
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document.write( "we know that 2x - y = 1 which means that 2 times the value of one jabr - 1 times the value of one al is equal to the cost of one typewriter.\r<BR>\n" );
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document.write( "by substitution, this equation becomes:\r<BR>\n" );
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document.write( "2*100 - y = 125\r<BR>\n" );
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document.write( "simplify to get 200 - y = 125\r<BR>\n" );
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document.write( "solve for y to get y = 75 dollars.\r<BR>\n" );
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document.write( "we know that x = 100 and y = 75\r<BR>\n" );
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document.write( "x is the value of one jabr<BR>\n" );
document.write( "y is the value of one al\r<BR>\n" );
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document.write( "1 jabr is worth 100 dollars because we said it was.\r<BR>\n" );
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document.write( "1 al is worth 75 dollars because we determined that from the equations.\r<BR>\n" );
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document.write( "the cost of 1 typewriter = 125 dollars because we determined that from the equations.\r<BR>\n" );
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document.write( "100/125 = 4/5 which means that one jabr is worth 4/5 * the cost of 1 typewriter.\r<BR>\n" );
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document.write( "75/125 = 3/5 which means that one al is worth 3/5 * the cost of 1 typewriter.\r<BR>\n" );
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document.write( "100/75 = 4/3 which means that the value of one jabr is worth 4/3 * the value of one al.\r<BR>\n" );
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document.write( "everything checks out so the solution is good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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