SOLUTION: An investment of $140,000 was made by a business club. The investment was split into three parts and lasted for 1 year. The first part of the invesment earned 8% interest, the sec
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Question 541630: An investment of $140,000 was made by a business club. The investment was split into three parts and lasted for 1 year. The first part of the invesment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $10440. The interest from the first investment was 2 times the interest from the second. Find the amount of the three parts of the investment. What is the amount of the first part of the investment? Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! partI x 8 %
part II y 6 %
part III z 9 %
Total Investment=$ 140000
Total interest from all =$ 10440
Interest from Part I is 2 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 = 2 * 0.06 y
0.08 x = 0.12 y
x= 1.5 y
0.06 y + 0.08 x + 0.09 z = 10440
But 0.08 x = 0.12 y
0.06 y + 0.12 y + 0.09 z = 10440
0.18 y + 0.09z = 10440 -------------- 1
Investment at
x+y+z= 140000
1.5 y+ 1 y + 1 z = 140000
2.5 y + 1 z = 140000 --------------2
0 y + 0.09 z = 10440 .............1
2.5 y + 1 z = 140000 .............2
Eliminate z
multiply (1)by 1
Multiply (2) by -0.09
0.18 y 0.09 z = 10440
-0.23 y + -0.09 z = -12600
Add the two equations
-0.04 y = -2160
/ -0.04
y = 48000.00
plug value of y in (1)
0.18 y + 0.09 z = 10440
8640 + 0.09 z = 10440
0.09 z = 10440 -8640
0.09 z = 1800
z = 20000.00
