Answer:
So $700 was invested in the mutual fund that earned a 2% profit, and $500 was invested in the mutual fund that earned a 5% profit.
Explanation:
Let x be the amount invested in the mutual fund that earned a 5% profit, and let y be the amount invested in the mutual fund that earned a 2% profit. We know that the total investment was $1,200, so:
x + y = 1200
We also know that the total profit was $39, which can be expressed as a decimal as 0.39 (since profit is calculated as a percentage of the initial investment). The amount of profit earned on the first fund is 5% of x, or 0.05x, and the amount of profit earned on the second fund is 2% of y, or 0.02y. So:
0.05x + 0.02y = 0.39
We now have two equations with two variables:
x + y = 1200
0.05x + 0.02y = 0.39
We can solve for one variable in terms of the other in the first equation, and substitute into the second equation:
x = 1200 - y
0.05(1200 - y) + 0.02y = 0.39
Simplifying and solving for y:
60 - 0.05y + 0.02y = 0.39
0.03y = 0.39 - 60
0.03y = -59.61
y = -59.61 / 0.03
y = 1987
This tells us that $1,987 was invested in the mutual fund that earned a 2% profit. To find the amount invested in the mutual fund that earned a 5% profit, we can substitute into the first equation:
x + y = 1200
x + 1987 = 1200
x = 1200 - 1987
x = -787
This doesn't make sense, since we can't have a negative investment amount. It means that we made a mistake somewhere. Checking our work, we can see that the equation 0.05x + 0.02y = 0.39 should actually be:
0.05x + 0.02y = 39
(without the decimal point). With this correction, we can solve as before:
x + y = 1200
0.05x + 0.02y = 39
x = 1200 - y
0.05(1200 - y) + 0.02y = 39
60 - 0.05y + 0.02y = 39
0.03y = 21
y = 700
So $700 was invested in the mutual fund that earned a 2% profit, and $500 was invested in the mutual fund that earned a 5% profit.