document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209489>Question 1209489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Musu Thorsen bought shares worth $10,000 in her employer’s profit-sharing scheme. When the share price rose by $10, she kept 1,000 shares and sold the rest for $11,000. How can you describe her share purchases? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848940 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can break down Musu Thorsen's share purchases and sales to describe the situation systematically.\r<BR>\n" );
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document.write( "### Let:<BR>\n" );
document.write( "- \( x \) = the original price per share.<BR>\n" );
document.write( "- \( n \) = the total number of shares Musu purchased.\r<BR>\n" );
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document.write( "### Step 1: Express the total value of her purchase.<BR>\n" );
document.write( "The total value of her purchase was $10,000. Thus:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "n \cdot x = 10,000<BR>\n" );
document.write( "\]<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "n = \frac{10,000}{x}<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "### Step 2: Calculate the number of shares sold.<BR>\n" );
document.write( "After the share price rose by $10, the new price per share became \( x + 10 \). Musu kept 1,000 shares, so the number of shares she sold was:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "n - 1,000 = \frac{10,000}{x} - 1,000<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "### Step 3: Express the total value of shares sold.<BR>\n" );
document.write( "The total value of the shares sold was $11,000. Therefore:<BR>\n" );
document.write( "\[<BR>\n" );
document.write( "\left( \frac{10,000}{x} - 1,000 \right)(x + 10) = 11,000<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "### Step 4: Solve for \( x \), the original share price.<BR>\n" );
document.write( "Simplify and solve this equation.\r<BR>\n" );
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document.write( "The original price per share (\( x \)) has two solutions: \r<BR>\n" );
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document.write( "\[<BR>\n" );
document.write( "x = -\frac{11}{2} + \frac{\sqrt{521}}{2} \quad \text{and} \quad x = -\frac{\sqrt{521}}{2} - \frac{11}{2}.<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "Since share prices must be positive, we consider only the first solution:\r<BR>\n" );
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document.write( "\[<BR>\n" );
document.write( "x = -5.5 + \frac{\sqrt{521}}{2}.<BR>\n" );
document.write( "\]\r<BR>\n" );
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document.write( "Let me compute the approximate numerical value of \( x \).\r<BR>\n" );
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document.write( "The original price per share was approximately **$5.91**. \r<BR>\n" );
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document.write( "### Description of her share purchases:<BR>\n" );
document.write( "1. **Total number of shares purchased:**  <BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   n = \frac{10,000}{x} \approx \frac{10,000}{5.91} \approx 1,692 \, \text{shares}.<BR>\n" );
document.write( "   \]\r<BR>\n" );
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document.write( "2. **Shares sold:**  <BR>\n" );
document.write( "   She kept 1,000 shares, so the number of shares sold was:  <BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   n - 1,000 \approx 1,692 - 1,000 = 692 \, \text{shares}.<BR>\n" );
document.write( "   \]\r<BR>\n" );
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document.write( "3. **New price per share after the $10 increase:**  <BR>\n" );
document.write( "   \[<BR>\n" );
document.write( "   x + 10 \approx 5.91 + 10 = 15.91 \, \text{dollars per share}.<BR>\n" );
document.write( "   \]\r<BR>\n" );
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document.write( "4. **Value of shares sold:**  <BR>\n" );
document.write( "   The 692 shares she sold at $15.91 each yielded approximately $11,000, as stated. \r<BR>\n" );
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document.write( "### Summary:  <BR>\n" );
document.write( "Musu initially bought about **1,692 shares** at **$5.91** per share. She kept **1,000 shares** and sold the remaining **692 shares** after the price rose to **$15.91**, earning $11,000 from the sale. </SPAN>\n" );
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