Question 552053: A person invested $42,000 in three different funds paying 5%, 7%, and 9% simple interest. The total annual interest from these investments was $2,600. The amount of money invested at 5% was $200 less than the amount invested at 7% and 9% combined. How much was invested in each fund? Check your solution.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Total = $42,000
5%,
7%,
and 9%
interest $2,600.
7% ----------x
9%-----------y
5%----------(x+y-200)
Total investment
x+y+x+y-200 = 42000
2x+2y=42000+200
2x+2y=42200
/2
x+y=21100................(1)
Interest
perecntages have been converted by multiplying the equation by 100
7x+9y+5(x+y-200)= 2600*100
7x+9y+5x+5y-1000=260000
12x+13y=260000+1000
12x+13y=261000..............(2)
1 x + 1 y = 21100 .............1
12 x + 13 y = 261000 .............2
Eliminate y
multiply (1)by -13
Multiply (2) by 1
-13 x -13 y = -274300
12 x 13 y = 261000
Add the two equations
-1 x = -13300
/ -1
x = 13300
plug value of x in (1)
1 x + 1 y = 21100
13300 + 1 y = 21100
1 y = 21100 -13300
1 y = 7800
y = 7800
x+y-200 = 13300+7800-200=21900
$13,300@ 7%
$7800 @ 9%
20,900 @ 5%
m.ananth@hotmail.ca
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