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. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $ 3150. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investment.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! 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
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