SOLUTION: An investment of ​$70 comma 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% inte

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Question 1153985: An investment of ​$70 comma 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 $ 5220. The interest from the first investment was 2 times the interest from the second. Find the amounts of the three parts of the investment.
The first part of the investment was ​$
2nd part $
Third part $
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Let Investment I be x @8%
Investment II be y @ 6%
and investment III be z @ 9%
Total investment
x+y+z=70000-----------1
Interest accrued
8%x+6%y+9%z = 5220
multiply by 100
we get
8x+6y+9z =522000-------2
8%x = 2*6%y
therefore 8x=12y
8x-12y=0 -------3


x + y + z = 70000
8 x + 6 y + 9 z = 522000

8 x -12 y = 0



consider equation 1 &2 Eliminate y
Multiply 1 by -6
Multiply 2 by 1
we get
-6 x -6 y -6 z = -420000
8 x + 6 y + 9 z = 522000
Add the two
2 x +3z = 102000 -------------4
consider equation 2 & 3 Eliminate y
Multiply 2 by 2
Multiply 3 by 1
we get
16 x + 12 y + 18 z = 1044000
8 x + -12 y = 0
Add the two
24 x +18z = 1044000 -------------5
Consider (4) & (5) Eliminate x
Multiply 4 by -12
Multiply (5) by 1
we get 2
-24 x -36 z = -1224000
24 x + 18 z = 1044000
Add the two
-18 z = -180000

z = 10000

Plug the value of z in (5)
24 x + 180000 = 1044000
24 x = 864000
x = 36000
plug value of x & z in 1
36000 + 1 y + 10000 = 70000
y = 70000 -36000 -10000
y= 24000
First investment $36000
II investment $24000
III investment $10000
Total $70,000

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

An investment of ​$70 comma 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 $ 5220. The interest from the first investment was 2 times the interest from the second. Find the amounts of the three parts of the investment.
The first part of the investment was ​$
2nd part $
Third part $
Let amount invested at 8% and 6% be E, and S, respectively

Then amount invested at 9% = 70,000 - E - S

We then have: .08E + .06S + .09(70,000 - E - S) = 5,220

.08E + .06S + 6,300 - .09E - .09S = 5,220

- .01E - .03S = - 1,080 ------ eq (i)



Also, 

- .01(1.5S) - .03S = - 1,080 ------- Substituting 1.5S for E in eq (i)

- .015S - .03S = - 1,080

- .045S = - 1,080

S, or amount invested at 6% =  

Now you can find the amounts invested at 6% and 9%. 

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