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An investor invested a total of $1,200 in two mutual funds. One fund earned a 5% profit while the other earned a 2% profit. If the investor’s total profit was $39, how much was invested in each mutual fund?

User Xonara
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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.

User Will Baker
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