document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79925>Question 79925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I need help in figuring out this problem. I can get some of it, I think I know how to get how many units in the case but not really sure. \r<BR>\n" );
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document.write( "The owner of a hobby store bought a case of 9-volt batteries for $26.00. He marked the price up such that his profit was $1.74 per battery. After selling 13 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?\r<BR>\n" );
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document.write( "thanks for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57324 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=57324\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are a couple of ways of looking at this problem.<BR>\n" );
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document.write( "First ... by selling 13 batteries the owner recovers the $26 that the case cost him.<BR>\n" );
document.write( "Let's find the price (P) he is charging per battery. That price times 13 batteries must<BR>\n" );
document.write( "equal $26. In equation form this becomes:<BR>\n" );
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document.write( "P * 13 = $26<BR>\n" );
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document.write( "Divide both sides by 13 to find the price being charged is:<BR>\n" );
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document.write( "P = $26/13 = $2 per battery.<BR>\n" );
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document.write( "But the owner has marked up the price per battery by $1.74.  So the original cost (C)<BR>\n" );
document.write( "to the owner was $2 - $1.74 = $0.26 or 26 cents per battery.<BR>\n" );
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document.write( "Then, at $0.26 per battery, how many batteries (B) can you get for $26.00. You can find<BR>\n" );
document.write( "the number of batteries (B) by dividing the total cost of $26 by the cost per battery (C) <BR>\n" );
document.write( "and you get:<BR>\n" );
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document.write( "B = $26/$0.26 = 100 batteries<BR>\n" );
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document.write( "Another way of looking at this problem is to let B equal the number of batteries in the case.<BR>\n" );
document.write( "Since the Cost of the entire case was $26 dollars, you can find the cost to the owner<BR>\n" );
document.write( "for each battery by dividing $26 by B.  So the owner paid $26/B per battery.<BR>\n" );
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document.write( "Then the owner increased this cost by $1.74 to establish the price he is asking for each<BR>\n" );
document.write( "battery. This makes the price per battery equal to ($26/B) + $1.74<BR>\n" );
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document.write( "When the owner sells 13 batteries at that price he takes in 13 times the price per battery<BR>\n" );
document.write( "and the problem says that amount is $26. So we can write the equation:<BR>\n" );
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document.write( "13 * [ (26/B) + 1.74] = 26<BR>\n" );
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document.write( "Do the distributive multiplication on the left side and you get:<BR>\n" );
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document.write( "[(13*26)/B] + [13*1.74] = 26<BR>\n" );
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document.write( "Since 13*26 = 338 and 13*1.74 = 22.62 this equation simplifies to:<BR>\n" );
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document.write( "[338/B] + 22.62 = 26<BR>\n" );
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document.write( "Subtract the 22.62 from both sides and you get:<BR>\n" );
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document.write( "[338/B] = 3.38<BR>\n" );
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document.write( "Eliminate the denominator by multiplying both sides by B to get:<BR>\n" );
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document.write( "338 = 3.38*B<BR>\n" );
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document.write( "And finally, solve for B by dividing both sides by 3.38 <BR>\n" );
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document.write( "B = 338/3.38 = 100<BR>\n" );
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document.write( "The answer to your problem is that there are 100 9-volt batteries in a case. Hopefully<BR>\n" );
document.write( "one of these ways will clarify the problem for you. And in the way of thinking about the<BR>\n" );
document.write( "economics of this situation, the owner has recovered the cost of the case of batteries<BR>\n" );
document.write( "by selling 13 of them.  That means the cash from the remaining 87 batteries can be used<BR>\n" );
document.write( "to cover other expenses of the store plus profit.  And at $2.00 per battery, that<BR>\n" );
document.write( "means the owner will take in $2 * 87 or $174 above his original cost of the batteries.<BR>\n" );
document.write( "(Presuming, of course, that he sells all the batteries before their expiration date.) </SPAN>\n" );
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