Question 1114157
An investment of ​$39,000 was made by a business club. The investment was split into three parts and lasted for one year.  Find the amounts of the three parts of the investment.

x+y+z=39000 ------------(1)

The first part (x)of the investment earned​ 8% interest,
 the second​ (y) at 6%,
 and the third​ (z) at 9%.

 Total interest from the investments was $ 3150. 
8%x+6%y+9%z=3150
8x+6y+9z=315000 -----------(2)
The interest from the first investment was 4 times the interest from the second.
8%x= 4*6%y 

8%x-24%y=0
8x-24y=0--------------------(3)

Solve the three equations

1	x	+	1	y	+	1	z	=	39000	
8	x	+	6	y		9	z	=	315000	
										
8	x	+	-24	y	+		0	z	0	
										
										
										
consider equation 1 &2				Eliminate y						
Multiply 1 by			-6				1			
Multiply 2 by			1				1			
we get										
-6	x		+	-6	y	+	-6	z	=	-234000
8	x		+	6	y	+	9	z	=	315000
Add the two										
2	x		+	0	y	+	3	z	=	81000
consider equation 2 & 3				Eliminate y						
Multiply 2 by				4						
Multiply 3 by				1						
we get										
32	x	+	24	y	+	36	z	=	1260000	
8	x	+	-24	y	+	0	z	=	0	
Add the two										
40	x	+	0	y	+	36	z	=	1260000	-------------5
Consider (4) & (5)			Eliminate x							
Multiply 4 by				-20						
Multiply (5) by				1						
we get				2						
-40	x	+	-60	z	=	-1620000				
40	x	+	36	z	=	1260000				
Add the two										
0	x	+	-24	z	=	-360000				
/										
z	=			15000      						
										
Plug the value of z in						(5)				
40	x	+	540000      		=	1260000				
40	x	=	720000      							
x	=			18000      						
plug value of x & z in					1					
18000      	+	1	y	+	15000      	=	39000			
1	y	=	39000      	+	-18000      	+	-15000      			
	y=	6000