Please help me slove this question.
An investor invested a total of $3,200 in tow mutual funds. One fund earned 5% profit while the other earned a 2% profit. If the invesor's total profit was $103, how much was invested in each mutual fund?
Tne amount invested in the mutual fund that earned 5% was $___?
The amount invested in th mutual fund that earned 2% was $____?
To solve this question, we can set up a system of equations. Let's call the amount invested in the mutual fund that earned 5% as "x" and the amount invested in the mutual fund that earned 2% as "y".
According to the question, the investor invested a total of $3,200, so we have the equation:
x + y = 3,200 (1)
We also know that the total profit earned by the investor was $103. The profit from the mutual fund that earned 5% is calculated as 5% of x and the profit from the mutual fund that earned 2% is calculated as 2% of y. So, we can write a second equation:
0.05x + 0.02y = 103 (2)
Now we can solve this system of equations using any method. In this case, we will use the substitution method. We will solve equation (1) for x, then substitute that value into equation (2) to find y.
From equation (1), we have:
x = 3,200 - y
Substituting this value of x into equation (2), we get:
0.05(3,200 - y) + 0.02y = 103
Simplifying the equation:
160 - 0.05y + 0.02y = 103
Combining like terms:
-0.03y = -57
Dividing by -0.03:
y = 1,900
Now, substitute the value of y back into equation (1):
x + 1,900 = 3,200
Subtracting 1,900 from both sides:
x = 1,300
Therefore, the amount invested in the mutual fund that earned 5% was $1,300 and the amount invested in the mutual fund that earned 2% was $1,900.