We should set up a system of linear equations to solve this. We will use variables, x and y, for the amount invested. We know the total amount invested is $9000. So we can say:
x + y = 9000
We also know that 3% of one of the investments plus 6% of the other is equal to $396. So we can say:
.03x + .06y = 396
This gives us a system of 2 linear equations with 2 variables. The hard part is now done.
Now we need to isolate one of variables in one of the equations and then do back substitution.
Lets isolate x in the first equation. This will give us:
x = 9000–y
We can now substitute 9000-y in the second equation where x is. This gives us:
.03(9000-y) + .06y = 396
Simplifying this equation we get:
270–.03y +.06y = 396
Now to get y by itself lets first subtract 270 from both sides to get:
—.03y + .06y = 126
Now we can add —.03y and .06y to get:
.03y = 126
Now divide both sides by .03 and we will have our y value.
y = 4200
Now that we have y lets go back to the first original equation and plug 4200 in for y in order to get our x value.
x + 4200 = 9000
Subtract both sides by 4200 to get:
x = 4800
So now we have it.
The amout invested that had a return of 3% is $4800 and the amount invested that had a return of 6% is $4200.