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?
:
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?