SOLUTION: 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 seco

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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 the investments
Answer by mananth(16946) About Me  (Show Source):
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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

m.ananth@hotmail.ca