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Question 1139884: An investment of $130 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 $ 9540. 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 $
nothing.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let the 3 investment amts = a, b, c
write an equation for each statement
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An investment of $130,000 was made by a business club.
The investment was split into three parts and lasted for one year.
a + b + c = 130000
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The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $ 9540.
.08a + .06b + .09c = 9540
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The interest from the first investment was 2 times the interest from the second.
.08a = 2(.06b)
.08a = .12b
a = .12b/.08
a = 1.5b
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Find the amounts of the three parts of the investment.
substitute 1.5b for a in the first equation
1.5b + b + c = 130000
2.5b + c = 130000
c = 130000-2.5b
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substitute .12b for .08a in the 2nd the equation
.12b + .06b + .09c = 9540
.18b + .09c = 9540
replace c with (130000-2.5b18)
.18b + .09(130000-2.5b) = 9540
.18b + 11700 - .225b = 9540
-.045b + 11700 = 9540
11700 - 9540 = .045b
2160 = .045b
b = 2160/.045
b = $48000 in b investment
then
c = 130000- 2.5(48000)
c = 130000 - 120000
c = $10000 in c investment
find a
130000 - 48000 - 10000 = $72000 in the a investment
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:
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Check the total interest
.08(72000) = 5760
.06(48000) = 2880
.09(10000) = 900
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total inter: $9540
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