An investor invested a total of
$1,900
in two mutual funds. One fund earned a
9%
profit while the other earned a
5%
profit. If the investor's total profit was
$143,
how much was invested in each mutual fund?
The amount invested in the mutual fund that earned
9%
was
what?
The amount invested in the mutual fund that earned
5%
was
what?
amount invested at 9% --- x
amount invested at 5% --- 1900-x
.09x + .05(1900-x) = 143
multiply by 100 to get rid of decimals
9x + 5(1900-x) = 14300
take over from here
To find the amounts invested in each mutual fund, we can use a system of equations.
Let's assume the amount invested in the mutual fund that earned 9% is x, and the amount invested in the mutual fund that earned 5% is y.
According to the given information:
x + y = 1900 -- equation 1 (since the total investment is $1900)
0.09x + 0.05y = 143 -- equation 2 (since the total profit is $143)
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method here:
Rearrange equation 1 to express x in terms of y:
x = 1900 - y
Substitute this value of x in equation 2:
0.09(1900 - y) + 0.05y = 143
Simplify and solve for y:
171 - 0.09y + 0.05y = 143
-0.04y = -28
y = (-28) / (-0.04)
y = 700
So, the amount invested in the mutual fund that earned 5% is $700.
Now, substitute this value of y back into equation 1 to find x:
x + 700 = 1900
x = 1900 - 700
x = 1200
Therefore, the amount invested in the mutual fund that earned 9% is $1200.
To summarize:
- The amount invested in the mutual fund that earned 9% is $1200.
- The amount invested in the mutual fund that earned 5% is $700.