document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199194>Question 1199194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> James spent $6780 on some watches and clocks. The amount spent on watches was $2820 more than the amount spent on the clocks. He bought 3/5 as many clocks as watches. Each clock cost $25 less than each watch. What was the total number of watches and clocks bought by James?\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 #832938 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given facts:<ol><li>James spent $6780 on some watches and clocks. </li><li>The amount spent on watches was $2820 more than the amount spent on the clocks. </li><li>He bought 3/5 as many clocks as watches. </li><li>Each clock cost $25 less than each watch. </li></ol>Let<BR>\n" );
document.write( "w = number of watches\r<BR>\n" );
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document.write( "Since 3/5 = 0.6, we can use fact 3 to say:<BR>\n" );
document.write( "0.6w = number of clocks\r<BR>\n" );
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document.write( "Now let<BR>\n" );
document.write( "x = cost of 1 watch<BR>\n" );
document.write( "which would mean<BR>\n" );
document.write( "x-25 = cost of 1 clock<BR>\n" );
document.write( "due to fact 4\r<BR>\n" );
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document.write( "1 watch = x dollars<BR>\n" );
document.write( "w number of watches = wx dollars<BR>\n" );
document.write( "1 clock = (x-25) dollars<BR>\n" );
document.write( "0.6w number of clocks = 0.6w(x-25) dollars\r<BR>\n" );
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document.write( "Add these subtotals to get $6780 spent on everything<BR>\n" );
document.write( "Refer to fact 1 above.<BR>\n" );
document.write( "watches + clocks = 6780 total<BR>\n" );
document.write( "wx + 0.6w(x-25) = 6780<BR>\n" );
document.write( "wx + 0.6wx - 0.6w*25 = 6780<BR>\n" );
document.write( "1.6wx - 15w = 6780<BR>\n" );
document.write( "Pause here for now. We'll come back to this later.\r<BR>\n" );
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document.write( "Fact 2 can be rephrased as:<BR>\n" );
document.write( "\"The amount spent on clocks was $2820 less than the amount spent on the watches\"<BR>\n" );
document.write( "which means:<BR>\n" );
document.write( "wx = amount spent on watches<BR>\n" );
document.write( "wx-2820 = amount spent on clocks\r<BR>\n" );
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document.write( "Those two subtotals also add to 6780, due to fact 1.<BR>\n" );
document.write( "wx+(wx-2820) = 6780<BR>\n" );
document.write( "2wx-2820 = 6780<BR>\n" );
document.write( "2wx = 6780+2820<BR>\n" );
document.write( "2wx = 9600<BR>\n" );
document.write( "wx = 9600/2<BR>\n" );
document.write( "wx = 4800<BR>\n" );
document.write( "Buying w number of watches, at x dollars a piece, cost $4800.\r<BR>\n" );
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document.write( "wx-2820 = 4800-2820 = 1980<BR>\n" );
document.write( "and the clocks cost $1980.\r<BR>\n" );
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document.write( "We'll now return to the previous equation we paused at.<BR>\n" );
document.write( "Plug in wx = 4800<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "1.6wx - 15w = 6780<BR>\n" );
document.write( "1.6(wx) - 15w = 6780<BR>\n" );
document.write( "1.6*(4800) - 15w = 6780<BR>\n" );
document.write( "7680 - 15w = 6780<BR>\n" );
document.write( "-15w = 6780-7680<BR>\n" );
document.write( "-15w = -900<BR>\n" );
document.write( "w = -900/(-15)<BR>\n" );
document.write( "w = 60<BR>\n" );
document.write( "James bought 60 watches.<BR>\n" );
document.write( "Each watch costs x = (wx)/w = 4800/60 = 80 dollars.\r<BR>\n" );
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document.write( "0.6w = number of clocks<BR>\n" );
document.write( "0.6w = 0.6*60<BR>\n" );
document.write( "0.6w = 36<BR>\n" );
document.write( "and he also bought 36 clocks.<BR>\n" );
document.write( "Each clock costs x-25 = 80-25 = 55 dollars.<BR>\n" );
document.write( "He spent 36*55 = 1980 dollars on clocks as mentioned earlier.\r<BR>\n" );
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document.write( "The two subtotals should add to 6780 dollars.<BR>\n" );
document.write( "watches + clocks = 4800+1980 = 6780<BR>\n" );
document.write( "This helps confirm the answers.\r<BR>\n" );
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document.write( "Further confirmation is to note that<BR>\n" );
document.write( "4800-1980 = 2820<BR>\n" );
document.write( "which matches up with fact 2\r<BR>\n" );
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document.write( "There's probably a much more faster/efficient way to solve this.<BR>\n" );
document.write( "Feel free to explore other options.\r<BR>\n" );
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document.write( "Answer: <BR>\n" );
document.write( "60 watches + 36 clocks<BR>\n" );
document.write( "96 total items.<BR>\n" );
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