document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177050>Question 1177050</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Rings and watches cost $10,275.00. The ratio of the number of watches to rings bought is 5:8. Each ring cost $137 more than a watch. The ratio of the total cost of the rings to watches bought was 7;8. Find the cost of a ring.<BR>\n" );
document.write( "Thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #805244 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=805244\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this problem doesn't work out as given.<BR>\n" );
document.write( "i keep getting a negative value for one of the variables.\r<BR>\n" );
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document.write( "i took a guess and figured that the ratio of watches to rings might actually be the ratio of rings to watches.\r<BR>\n" );
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document.write( "this allowed me to get a solution that made more sense because it was positive and the numbers worked out.\r<BR>\n" );
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document.write( "here's how it went after making that assumption.\r<BR>\n" );
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document.write( "let x = the number of rings.<BR>\n" );
document.write( "let y = the number of watches.\r<BR>\n" );
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document.write( "let r = cost of a ring.<BR>\n" );
document.write( "let w = cost of a watch.\r<BR>\n" );
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document.write( "the ratio of the number of rings to watches is 5/8.\r<BR>\n" );
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document.write( "the equation for that is x/y = 5/8.\r<BR>\n" );
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document.write( "the total cost of rings is equal to x * r.<BR>\n" );
document.write( "the total cost of watches is equal to y * w.\r<BR>\n" );
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document.write( "the cost of a ring is equal to the cost of a watch plus 137 dollars.\r<BR>\n" );
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document.write( "the formula for this is r = w + 137.\r<BR>\n" );
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document.write( "you are also given that the ratio of the total cost of rings to the total cost of watches is 7/8.\r<BR>\n" );
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document.write( "the equation for this is x * r / y * w = 7/8\r<BR>\n" );
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document.write( "you have the following ratios:\r<BR>\n" );
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document.write( "x / y = 5/8<BR>\n" );
document.write( "x * r / y * w = 7/8\r<BR>\n" );
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document.write( "from these ratios, you can derive the following:\r<BR>\n" );
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document.write( "x = 5/8 * y<BR>\n" );
document.write( "x * r = 7/8 * y * w\r<BR>\n" );
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document.write( "you are also given that the total cost of the rings plus the total cost of the watches is 10275.\r<BR>\n" );
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document.write( "the equation for this is x * r + y * w = 10275.\r<BR>\n" );
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document.write( "since x * r = 7/8 * y * w, the equation of x * r + y * w = 10275 becomes:<BR>\n" );
document.write( "7/8 * y * w + y * w = 10275.<BR>\n" );
document.write( "factor out the y * w to get:<BR>\n" );
document.write( "y * w * (7/8 + 1) = 10275.<BR>\n" );
document.write( "since 1 = 8/8, this becomes:<BR>\n" );
document.write( "y * w * (7/8 + 8/8) = 10275.<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "y * w * 15/8 = 10275.\r<BR>\n" );
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document.write( "solve for y * w to get y * w = 8/15 * 10275 = 5480.\r<BR>\n" );
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document.write( "this means that x * r must be equal  to 10275 - 5480 = 4795.\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "x * r = 4795<BR>\n" );
document.write( "y * w = 5480\r<BR>\n" );
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document.write( "since x = 5/8 * y, these equations become:\r<BR>\n" );
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document.write( "5/8 * y * r = 4795<BR>\n" );
document.write( "y * w = 5480\r<BR>\n" );
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document.write( "since r = w + 137, these equations becomes:\r<BR>\n" );
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document.write( "5/8 * y * (w + 137) = 4795<BR>\n" );
document.write( "y * w = 5480.\r<BR>\n" );
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document.write( "simplify these equations to get:\r<BR>\n" );
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document.write( "5/8 * y * w + 5/8 * y * 137 = 4795<BR>\n" );
document.write( "y * w = 5480.\r<BR>\n" );
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document.write( "in the first of these 2 equations, replace y * w with 5480 from the second of these two equations to get:\r<BR>\n" );
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document.write( "5/8 * 5480 + 5/8 * y * 137 = 4795.\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "3425 + 85.625 * y = 4795\r<BR>\n" );
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document.write( "subtract 3425 from both sides of this equation to get:\r<BR>\n" );
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document.write( "85.625 * y = 1370\r<BR>\n" );
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document.write( "solve for y to get:\r<BR>\n" );
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document.write( "y = 1370 / 85.625 = 16.\r<BR>\n" );
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document.write( "since the ratio of x to y is 5/8, then you get x = 10.\r<BR>\n" );
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document.write( "you have x = 10 and y = 16.\r<BR>\n" );
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document.write( "since x * r = 4795, then r must be equal to 4795 / 10 = 479.5\r<BR>\n" );
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document.write( "since y * w = 5480, then w must be equal to 5480 / 16 = 342.5\r<BR>\n" );
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document.write( "your solution looks like it will be that the cost of a ring is 479.5.\r<BR>\n" );
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document.write( "to confirm that the solution is correct, i did the following.\r<BR>\n" );
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document.write( "cost of a ring is 479.5<BR>\n" );
document.write( "cost of a watch is 342.5\r<BR>\n" );
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document.write( "cost of a ring is 137 more than a watch.<BR>\n" );
document.write( "342.5 + 137 = 479.5<BR>\n" );
document.write( "this part checks out.\r<BR>\n" );
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document.write( "total cost of rings is 10 * 479.5 = 4795.<BR>\n" );
document.write( "total cost of watches is 16 * 342.5 = 5480.<BR>\n" );
document.write( "total cost of both is 4795 + 5480 = 10275.<BR>\n" );
document.write( "this part checks out.\r<BR>\n" );
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document.write( "the ratio of the number of rings to watches is 5/8.<BR>\n" );
document.write( "10/16 = 5/8.<BR>\n" );
document.write( "this part checks out.\r<BR>\n" );
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document.write( "the ratio of the total cost of rings to total cost of watches is 7/8.<BR>\n" );
document.write( "4795/5480 = 7/8.<BR>\n" );
document.write( "this part checks out.\r<BR>\n" );
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document.write( "all the parts check out, indicating that the solution is correct.\r<BR>\n" );
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document.write( "since you were asked for the cost of a ring, then your solution is that the cost of a ring is 479.5.\r<BR>\n" );
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document.write( "this solution was only possible when i assumed that the ratio of the number of rings to watches is 5/8 and not that the ratio of the number of watches to rings is 5/8.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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