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mathstudent55
He invested two unknown amount that add to $1200.
Let the amount invested at 9% be x.
Let the amount invested at 3% be y.

The amounts add to $1200.
x + y = 1200           First Equation

The profit from the 9% part is 0.09x.
The profit from the 3% part is 0.03y.
The two profits add to $78.
0.09x + 0.03y = 78        Second Equation

We have two equations in two unknowns, so we can solve this problem as a system of equations.

x + y = 1200
0.09x + 0.03y = 78

Multiply the first equation by -0.09 and add to the second equation.

-0.09x - 0.09y = -108
 0.09x + 0.03y =   78
----------------------------
             -0.06y = -30

Divide both sides by -0.06

y = 500

Now we substitute 500 into y in the first equation.

x + y = 1200

x + 500 = 1200

x = 700

Answer: The amount invested at 9% is $700
lilxiong
Hey there!

To start, let x represent the cost of the mutual fund that earned 9%.

This cost will be represented by the term 0.09x.

Now, let (1200-x) represent the cost of the mutual fund that earned 3% profit, since the two amounts must add up to be 1200, the amount the investor originally invested. 

This cost will be represented by 0.03(1200-x)

Next, because the overall profit of the two mutual funds earned was 78 dollars, you can set up this equation:
0.09x+0.03(1200-x)=78

Now, solve for the value of x:
0.09x+0.03(1200-x)=78
0.09x+36-0.03x=78
0.06x+36=78
0.06x=42
x=700

Therefore, the amount invested in the 9% mutual fund would be $700 dollars.

Hope this helps and have a wonderful day! :)

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