SOLUTION: $10,000 is to be invested in three different ways. One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice

Question 607390: $10,000 is to be invested in three different ways. One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice the first, is used to buy government bonds at 9% per year. The remainder is put in the bank at 5% annual interest. In the first year, the investments bring a return of $830. How much was invested in each way?
This is a matrices problem but I am confused with how to begin with the equations.
Is one equation x + y + z = 10,000? The second equation.. Is is something like this? 0.08x + 2(0.09)y =
I will be able to solve the problem after understanding how to put the wording into equations.. I understand how to solve matrices, so I am not asking for help with that. Thank you.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
$10,000 is to be invested in three different ways.
One part of the money is used to purchase mutual fund that offer a return of 8% per year.
The second part, which amounts to twice the first, is used to buy government bonds at 9% per year.
The remainder is put in the bank at 5% annual interest.
In the first year, the investments bring a return of $830.
How much was invested in each way?
:
Let x = amt invested at 8%
Let y = amt invested at 9%
Let z = amt invested at 5%
:
"$10,000 is to be invested in three different ways."
x + y + z = 10000
:
"One part of the money is used to purchase mutual fund that offer a return of 8% per year. The second part, which amounts to twice the first, is used to buy government bonds at 9% per year."
y = 2x
-2x + y = 0
:
" the first year, the investments bring a return of $830.
.08x + .09y + .05z = 830
:
From these three equations we can derive a matrix
1, 1, 1, 10000
-2, 1, 0, 0
.08, .09, .05, 830

How much was invested in each way?
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