document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103973>Question 1103973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two brothers A and B have their annual incomes in the ratio of 8:5 while their annual spending is in the ratio 5:3. \r<BR>\n" );
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document.write( "If they save $1,200 and $1,000 respectively, find their annual incomes.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #718698 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=718698\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have:\r<BR>\n" );
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document.write( "ratio of income of A to income of B = 8/5.\r<BR>\n" );
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document.write( "ratio of spending of A to spending of B = 5/3.\r<BR>\n" );
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document.write( "A saves 1200.\r<BR>\n" );
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document.write( "B saves 1000.\r<BR>\n" );
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document.write( "all figures are annual figures.\r<BR>\n" );
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document.write( "let x = income of A.\r<BR>\n" );
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document.write( "let y = income of B.\r<BR>\n" );
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document.write( "ratio of income of A to income of B becomes x/y = 8/5\r<BR>\n" );
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document.write( "solve for y to get y = 5x/8.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "income of A = x<BR>\n" );
document.write( "income of B = 5x/8.\r<BR>\n" );
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document.write( "the variable of y disappears from the income ratio and therefore can be used again in the spending ratio.\r<BR>\n" );
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document.write( "let y = spending of A.\r<BR>\n" );
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document.write( "let z = spending of B.\r<BR>\n" );
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document.write( "ratio of spending of A to spending of B becomes y/z = 5/3\r<BR>\n" );
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document.write( "solve for z to get z = 3y/5\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "spending of A = y<BR>\n" );
document.write( "spending of B = 3y/5\r<BR>\n" );
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document.write( "the variable of z disappears from the spending ratio and therefore can be used again in the saving ratio.\r<BR>\n" );
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document.write( "however, we won't need it anymore because we have the figures for the saving of A and the saving of B.\r<BR>\n" );
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document.write( "the saving of A = 1200; the spending of A = y; the income of A = x.\r<BR>\n" );
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document.write( "since income minus spending = saving, you get:\r<BR>\n" );
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document.write( "x - y = 1200\r<BR>\n" );
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document.write( "the saving of B = 1000; the spending of B = 3y/5; the income of B = 5x/8.\r<BR>\n" );
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document.write( "since income minus spending = saving, you get:\r<BR>\n" );
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document.write( "5x/8 - 3y/5 = 1000\r<BR>\n" );
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document.write( "you have two equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "x - y = 1200 (equation 1)<BR>\n" );
document.write( "5x/8 - 3y/5 = 1000 (equation 2)\r<BR>\n" );
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document.write( "multiply both sides of equation 2 by 40 to get:\r<BR>\n" );
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document.write( "25x - 24y = 40,000 (equation 3)\r<BR>\n" );
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document.write( "your equations to solve simultaneously are now:\r<BR>\n" );
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document.write( "x - y = 1200 (equation 1)<BR>\n" );
document.write( "25x - 24y = 40,000 (equation 3)\r<BR>\n" );
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document.write( "multiply both sides of equation 1 by 25 to get:\r<BR>\n" );
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document.write( "25x - 25y = 30,000 (equation 4)\r<BR>\n" );
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document.write( "your equations to solve simultaneosly are now:\r<BR>\n" );
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document.write( "25x - 24y = 40,000 (equation 3)<BR>\n" );
document.write( "25x - 25y = 30,000 (equation 4)\r<BR>\n" );
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document.write( "subtract equation 4 from equation 3 to get:\r<BR>\n" );
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document.write( "y = 10,000\r<BR>\n" );
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document.write( "go back to equation 1 and solve for x.\r<BR>\n" );
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document.write( "start with x - y = 1200 (equation 1)<BR>\n" );
document.write( "replace y with 10,000 to get:<BR>\n" );
document.write( "x - 10,000 = 1200<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 11,200\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "x = 11,200 and y = 10,000\r<BR>\n" );
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document.write( "11,200 is the income of A.<BR>\n" );
document.write( "10,000 is the spending of A.<BR>\n" );
document.write( "1200 is the saving of A.\r<BR>\n" );
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document.write( "income minus spending = savings, therefore:\r<BR>\n" );
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document.write( "11,200 - 10,000 = 1200, confirming the income and spending of A is correct.\r<BR>\n" );
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document.write( "from equation 2, you find that:\r<BR>\n" );
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document.write( "income of B = 5x/8<BR>\n" );
document.write( "spending of B = 3y/8\r<BR>\n" );
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document.write( "since x = 11,200, then 5x/8 = 7000.<BR>\n" );
document.write( "since y = 10,000, then 3y/5 = 6000.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "income of B = 7000<BR>\n" );
document.write( "spending of B = 6000\r<BR>\n" );
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document.write( "saving of B = income of B minus spending of B, therefore:\r<BR>\n" );
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document.write( "7000 - 6000 = 1000.\r<BR>\n" );
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document.write( "this confirms income and spending for B are correct.\r<BR>\n" );
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document.write( "you wind up with:\r<BR>\n" );
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document.write( "income of A = 11,200<BR>\n" );
document.write( "spending of A = 10,000<BR>\n" );
document.write( "saving of A = 1,200\r<BR>\n" );
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document.write( "income of B = 7,000<BR>\n" );
document.write( "spending of B = 6,000<BR>\n" );
document.write( "saving of B = 1,000\r<BR>\n" );
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document.write( "income ratio of A/B = 11,200 / 7,000 which simplifies to 8/5.\r<BR>\n" );
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document.write( "spending ratio of A/B = 10,000 / 6,000 which simplifies to 5/3.\r<BR>\n" );
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document.write( "requirements of the problem are satisfied.\r<BR>\n" );
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document.write( "your solution is that income of A = $11,200 and income of B = $7,000.\r<BR>\n" );
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