document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=739904>Question 739904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  Solve the following simple interest word problem:\r<BR>\n" );
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document.write( "Sue, a recent retiree, requires $6,000 per year in extra income.  She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year.  How much money should be invested in each to realize exactly $6,000 in interest per year?\r<BR>\n" );
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document.write( "2.  Solve the following time-distance word problem:\r<BR>\n" );
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document.write( "A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour (mi/hr).  The trip up and back takes 6 hours.  Assuming that the motor boat maintained a constant speed relative to the water, what was its speed?<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 #451412 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=451412\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Part I	15.00%		per annum	-------------	Amount invested =x					<BR>\n" );
document.write( "Part II	7.00%		per annum	------------	Amount invested = y					<BR>\n" );
document.write( "	50000									<BR>\n" );
document.write( "Interest-----	6000.00									<BR>\n" );
document.write( "										<BR>\n" );
document.write( "Part I	15.00%		per annum	---x					*	<BR>\n" );
document.write( "Part II	7.00%		per annum	---y						<BR>\n" );
document.write( "Total investment										<BR>\n" );
document.write( "x	+	1	y=	50000	-------------1					<BR>\n" );
document.write( "Interest on both investments										<BR>\n" );
document.write( "15.00%	x	+	7.00%	y=	6000					<BR>\n" );
document.write( "Multiply by		100								<BR>\n" );
document.write( "15	x	+	7	y=	600000.00	--------2				<BR>\n" );
document.write( "Multiply (1) by			-15							<BR>\n" );
document.write( "we get										<BR>\n" );
document.write( "-15	x	-15	y=	-750000.00						<BR>\n" );
document.write( "Add this to (2)										<BR>\n" );
document.write( "0	x	-8	y=	-150000						<BR>\n" );
document.write( "divide by		-8								<BR>\n" );
document.write( "			y	=	18750				 -	x)<BR>\n" );
document.write( "Part I	15.00%	$	31250							<BR>\n" );
document.write( "Part II	7.00%	$	18750							<BR>\n" );
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document.write( "CHECK										<BR>\n" );
document.write( "31250	---------	15.00%	-------	4687.50						<BR>\n" );
document.write( "18750	-------------	7.00%	-------	1312.50						<BR>\n" );
document.write( "Total			--------------------	6000.00						<BR>\n" );
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document.write( "Boat speed	x	mph											<BR>\n" );
document.write( "current speed	3	mph											<BR>\n" );
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document.write( "Distance with wind	24	miles											<BR>\n" );
document.write( "Distance against wind	24	miles											<BR>\n" );
document.write( "													<BR>\n" );
document.write( "spee with current	x	+	3	mph									<BR>\n" );
document.write( "speed against	x		3	mph									<BR>\n" );
document.write( "Total   time =		6	hours										<BR>\n" );
document.write( "Time with current=		24	/(	x	+	25	)						<BR>\n" );
document.write( "time against current		24	/	(	x	-25	)						<BR>\n" );
document.write( "													<BR>\n" );
document.write( "Time with  current + time against  =			10	hours									<BR>\n" );
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document.write( "24	/(	x	+	3	)	+	24	/(x	-3	)	=	6	<BR>\n" );
document.write( "LCD =	(	x	+	3	)*	(x	-3	)					<BR>\n" );
document.write( "multiply the equation by the LCD													<BR>\n" );
document.write( "we get													<BR>\n" );
document.write( "24	*	(x	-3	)+	24	(x	+	3	)=	6	(x^2-	9	)<BR>\n" );
document.write( "24	x	-72	+	24	x	+	72	)=	6	X^2		54	<BR>\n" );
document.write( "48	x	0	=	10	X^2		-54						<BR>\n" );
document.write( "6	X^2	-48	x	0	+	-54	=	0					<BR>\n" );
document.write( "6	X^2+	-48	x+	-54	=	0							OK<BR>\n" );
document.write( "/	1												<BR>\n" );
document.write( "6	X^2	-48	x	-54	=	0							<BR>\n" );
document.write( "													<BR>\n" );
document.write( "	Find the roots of the equation by quadratic formula												<BR>\n" );
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document.write( "	a=	6	b=	-48	c=	-54							<BR>\n" );
document.write( "													<BR>\n" );
document.write( "	b^2-4ac=	2304	-	-1296									<BR>\n" );
document.write( "	b^2-4ac=	3600			<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%093600%09%29 ALIGN=MIDDLE  ALT=\"sqrt%28%093600%09%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=	60					=<BR>\n" );
document.write( "	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >												<BR>\n" );
document.write( "	<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >												<BR>\n" );
document.write( "	x1=(	48	+	60	)/	12							<BR>\n" );
document.write( "	x1=	9											<BR>\n" );
document.write( "	x2=(	48	-60	) /	12								<BR>\n" );
document.write( "	x2=	-1											<BR>\n" );
document.write( "	Ignore negative value			mph									<BR>\n" );
document.write( "	x	=	9										<BR>\n" );
document.write( "			\r<BR>\n" );
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document.write( "							<BR>\n" );
document.write( "m.ananth@hotmail.ca										<BR>\n" );
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