document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006346>Question 1006346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag of batteries in the ratio of 3 size D batteries to 7 size C batteries is combined with a bag having a ratio of 5 size D to 1 size C.\r<BR>\n" );
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document.write( "If the two bags together now contain an equal number of size D and C batteries, how many batteries are in the second bag?\r<BR>\n" );
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document.write( "My attempt:<BR>\n" );
document.write( "Step 1: I can see that the first bag in the ratio of 3/7 has 18 size D batteries and 42 size C batteries, given that the total number in the bag is 60.\r<BR>\n" );
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document.write( "Step 2: I can see that the second bag is in the ratio of 5/1.\r<BR>\n" );
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document.write( "Step 3: Through trial and error, I can see that I need to get to a combined bag with a ratio of 8/8 for a total of 96. But I don't know how to do this mathematically. \r<BR>\n" );
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document.write( "This is often my problem. Can anybody help me set this up?\r<BR>\n" );
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document.write( "Thank you. \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 #622515 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=622515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are correct in that both bags will contain 96 batteries.<BR>\n" );
document.write( "there will be 48 D and 48 C.\r<BR>\n" );
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document.write( "you are given that the first bag contains 60 batteries total and that the ratio of D to C is 3/7\r<BR>\n" );
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document.write( "let x = the common multiplier.\r<BR>\n" );
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document.write( "you get 3x + 7x = 60\r<BR>\n" );
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document.write( "combine like terms to get 10x = 60\r<BR>\n" );
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document.write( "solve for x to get x = 6\r<BR>\n" );
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document.write( "the common multiplier is 6.\r<BR>\n" );
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document.write( "3*6 + 7*6 = 18 + 42 = 60\r<BR>\n" );
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document.write( "the total number of batteries is 60.\r<BR>\n" );
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document.write( "the ratio of D to C is 18 / 42 = 3 / 7.\r<BR>\n" );
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document.write( "the batteries in the second bag are in the ratio of D / C = 5 / 1\r<BR>\n" );
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document.write( "let y be the common multiplier for the second bag.\r<BR>\n" );
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document.write( "you get 5y + 1y = z\r<BR>\n" );
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document.write( "z is the total for the second bag.\r<BR>\n" );
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document.write( "when you add the D batteries together and you add the C batteries together, you will get a ratio of 1/1.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "(18 + 5y) / (42 + y) = 1/1 which becomes:\r<BR>\n" );
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document.write( "(18 + 5y) / (42 + y) = 1\r<BR>\n" );
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document.write( "multiply both sides of this equation by (42 + y) to get\r<BR>\n" );
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document.write( "18 + 5y = 42 + y\r<BR>\n" );
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document.write( "subtract y from both sides of this equation and subtract 18 from both sides of this equation to get:\r<BR>\n" );
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document.write( "5y - y = 42 - 18\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "4y = 24\r<BR>\n" );
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document.write( "solve for y = get y = 6\r<BR>\n" );
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document.write( "when y = 6, the equation for your second bag of 5y + y = z becomes 30 + 6 = z which results in 36 = z\r<BR>\n" );
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document.write( "your second bag contains 36 batteries.<BR>\n" );
document.write( "30 of them are D<BR>\n" );
document.write( "6 of them are C.<BR>\n" );
document.write( "the ratio of D/C = 30/6 = 5/1.\r<BR>\n" );
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document.write( "your combined bag contains 60 + 36 = 96 batteries.<BR>\n" );
document.write( "your total D are 18 + 30 = 48<BR>\n" );
document.write( "your total C are 42 + 6 = 48<BR>\n" );
document.write( "the ratio of D to C is 1/1.\r<BR>\n" );
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