An investor invested a total of 2900 in two mutual funds. One fund earned a 9% profit the other earned a 5% profit. If the investors total profit was $217 how much was invested in each mutual fund.
if x was invested at 9%, then 2900-x was invested at 5%.
.09x + .05(2900-x) = 217
x = 1800
so, $1800 at 9%, $1100 at 5%
To solve this problem, we can use a system of equations. Let's denote the amount invested in the mutual fund that earned a 9% profit as x, and the amount invested in the mutual fund that earned a 5% profit as y.
We know that the investor invested a total of $2900, so the first equation is:
x + y = 2900
The second equation is formed based on the total profit of $217. The profit from the first fund is 9% of x, and the profit from the second fund is 5% of y, so:
0.09x + 0.05y = 217
Now we have a system of two equations with two variables. To solve this system, we can use the method of substitution or elimination.
Let's solve it using the substitution method. We rearrange the first equation to express y in terms of x:
y = 2900 - x
Substituting this expression for y in the second equation:
0.09x + 0.05(2900 - x) = 217
Simplifying the equation:
0.09x + 145 - 0.05x = 217
Combine like terms:
0.04x = 217 - 145
0.04x = 72
Divide by 0.04 to solve for x:
x = 72 / 0.04
x = 1800
Now we substitute the value of x back into the first equation to find y:
1800 + y = 2900
y = 2900 - 1800
y = 1100
Therefore, the investor invested $1800 in the mutual fund that earned a 9% profit and $1100 in the mutual fund that earned a 5% profit.