An investor invested a total of $3,400 in two mutual funds. One fund earned 8% profit while the other earned a 3% profit. If the investor's total profit was $202, how much was invested in each mutual fund?
amount invested at 8% ---- x
amount invested at 3% ---- 3400-x
solve for x
.08x + .03(3400-x) = 202
8x + 3(3400-x) = 20200
....
....
x = ....
To solve this problem, we can use a system of equations.
Let's assume the amount invested in the fund that earned 8% profit is x dollars, while the amount invested in the fund that earned 3% profit is y dollars.
According to the problem, the total amount invested is $3,400, so we have the equation:
x + y = 3400 .....(equation 1)
The total profit earned is $202. The profit earned from the fund that earned 8% profit can be calculated by multiplying the amount invested (x) by 8% (0.08), while the profit earned from the fund that earned 3% profit can be calculated by multiplying the amount invested (y) by 3% (0.03). Therefore, we have the second equation:
0.08x + 0.03y = 202 .....(equation 2)
Now we can solve the system of equations consisting of equation 1 and equation 2.
To eliminate decimals, we can multiply equation 2 by 100:
8x + 3y = 20200 .....(equation 3)
Now we have a system of equations:
x + y = 3400 .....(equation 1)
8x + 3y = 20200 .....(equation 3)
We can solve this system of equations by substitution or elimination. Let's use elimination.
Multiply equation 1 by 3:
3x + 3y = 10200 .....(equation 4)
Now we can subtract equation 4 from equation 3 to eliminate y:
(8x + 3y) - (3x + 3y) = 20200 - 10200
8x - 3x = 10000
5x = 10000
x = 10000/5
x = 2000
Now we can substitute the value of x into equation 1 to find y:
2000 + y = 3400
y = 3400 - 2000
y = 1400
So, $2000 was invested in the fund that earned 8% profit, while $1400 was invested in the fund that earned 3% profit.