document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168239>Question 1168239</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	A manufacturer sells kayaks to dealers for Php 94,500 with discounts of 40/10/5.<BR>\n" );
document.write( "a.	Determine the net price of a kayak.<BR>\n" );
document.write( "b.	How much is the total trade discount?<BR>\n" );
document.write( "c.	What is the equivalent single trade discount for this transaction?<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 #851663 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=851663\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the list price of a kayak be $L = \text{Php } 94,500$.<BR>\n" );
document.write( "The discounts offered are 40/10/5. This means there are three successive discounts.\r<BR>\n" );
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document.write( "**a. Determine the net price of a kayak.**\r<BR>\n" );
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document.write( "To find the net price, we apply the discounts sequentially to the original price.\r<BR>\n" );
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document.write( "1.  **First discount (40%):**<BR>\n" );
document.write( "    Discount amount = $40\% \times 94,500 = 0.40 \times 94,500 = \text{Php } 37,800$<BR>\n" );
document.write( "    Price after the first discount = $94,500 - 37,800 = \text{Php } 56,700$\r<BR>\n" );
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document.write( "2.  **Second discount (10%):**<BR>\n" );
document.write( "    This discount is applied to the price after the first discount.<BR>\n" );
document.write( "    Discount amount = $10\% \times 56,700 = 0.10 \times 56,700 = \text{Php } 5,670$<BR>\n" );
document.write( "    Price after the second discount = $56,700 - 5,670 = \text{Php } 51,030$\r<BR>\n" );
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document.write( "3.  **Third discount (5%):**<BR>\n" );
document.write( "    This discount is applied to the price after the second discount.<BR>\n" );
document.write( "    Discount amount = $5\% \times 51,030 = 0.05 \times 51,030 = \text{Php } 2,551.50$<BR>\n" );
document.write( "    Net price = $51,030 - 2,551.50 = \text{Php } 48,478.50$\r<BR>\n" );
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document.write( "Alternatively, we can calculate the net price using the discount factors:<BR>\n" );
document.write( "Net price = List price $\times (1 - \text{discount}_1) \times (1 - \text{discount}_2) \times (1 - \text{discount}_3)$<BR>\n" );
document.write( "Net price = $94,500 \times (1 - 0.40) \times (1 - 0.10) \times (1 - 0.05)$<BR>\n" );
document.write( "Net price = $94,500 \times (0.60) \times (0.90) \times (0.95)$<BR>\n" );
document.write( "Net price = $94,500 \times 0.513$<BR>\n" );
document.write( "Net price = $\text{Php } 48,478.50$\r<BR>\n" );
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document.write( "**b. How much is the total trade discount?**\r<BR>\n" );
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document.write( "The total trade discount is the difference between the original list price and the net price.<BR>\n" );
document.write( "Total trade discount = List price - Net price<BR>\n" );
document.write( "Total trade discount = $94,500 - 48,478.50 = \text{Php } 46,021.50$\r<BR>\n" );
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document.write( "**c. What is the equivalent single trade discount for this transaction?**\r<BR>\n" );
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document.write( "The equivalent single trade discount is the single discount rate that would give the same net price. Let the equivalent single discount rate be $d$.<BR>\n" );
document.write( "Net price = List price $\times (1 - d)$<BR>\n" );
document.write( "$48,478.50 = 94,500 \times (1 - d)$<BR>\n" );
document.write( "$1 - d = \frac{48,478.50}{94,500}$<BR>\n" );
document.write( "$1 - d = 0.513$<BR>\n" );
document.write( "$d = 1 - 0.513$<BR>\n" );
document.write( "$d = 0.487$\r<BR>\n" );
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document.write( "To express this as a percentage, we multiply by 100:<BR>\n" );
document.write( "Equivalent single trade discount = $0.487 \times 100\% = 48.7\%$\r<BR>\n" );
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document.write( "Final Answer: The final answer is $\boxed{a. \text{Php } 48,478.50, b. \text{Php } 46,021.50, c. 48.7\%}$ </SPAN>\n" );
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