Question 582824
An investment of 62,000 was made by a business club. The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest the second 6% and the third 9%. The total interest from the investment was 4740. The interest from the first investment was 6 times the interest from the second. Find the amounts of the three parts of 

partI	x	8	%						
part II	y	6	%						
part III	z	9	%						
Total Investment=$ 62000						
Total interest from all =$4740						
Interest from Part I is	6	times interest from Part II					
									
Interest from		part II	=	0.06	y 				
Interest from  		partI	=	0.08	x				
Interest from		part III	=	0.09	z				
0.08	x	=	6	*	0.06	y 			
0.08	x	=	0.36	y 					
x=	4.5y 
							
0.06	y 	+	0.08	x	+	0.09	z	=	4740
But	0.08	x	=	0.36	y 				
0.06	y	+	0.36	y 	+	0.09	z	=	4740

0.42	y 	+	0.09	z=	4740		-------------- 1		
									
Investment at									
x+y+z=	62000		x=4.5y 
				
4.5y+y	+z=	62000	
5.5y+z	=62000	--------------2		
									
0.42	y 	+	0.09	z	=	4740	.............1		
5.5	y 	+	1.00	z	=	62000	.............2		
Eliminate	z								
multiply (1)by		-1							
Multiply (2) by		0.09
							
-0.42	y 		-0.09	z	=	-4740			
0.5	y 	+	0.09	z	=	5580			
Add the two equations									
0.08y =840			
/0.08								
y 	=	11200.00							
plug value of			y 	In (2)					
5.5	y 	+	1	z	=	62000			
61600		+	1	z	=	62000			
			1	z	=	62000-61600	
			1	z	=	400			
				z	=	400		
									
x+y+z=	62000								
									
x=	62000	-(11200	+400)
x=	50400								
									
CHECK									
									
	amount  	Rate		Interest  					
x =	50400 -	8%--	4032					
y=	11200	-6%--	672					
z=	400	-9%--	36					
Total  	62000	--		4740					
									
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