Question

An investor invested a total of ​$1,400 in two mutual funds. One fund earned a 9​% profit while the other earned a 2​% profit. If the​ investor's total profit was ​$49​, how much was invested in each mutual​ fund?

Answer 1

To find the amount invested in each mutual fund, we need to set up and solve a system of equations. Let x be the amount invested at a 9% profit and y be the amount invested at a 2% profit, with the total investment being $1,400 and the total profit being $49. Through substitution and simplification, we can solve for x and y to determine the individual investments.

Step-by-step explanation:

The subject of the student's question is investment in the context of mutual funds and profit calculation, which falls under the category of Mathematics. Specifically, it touches on the topic of algebraic equations and percentage profits.

To solve the problem, we let x represent the amount invested in the mutual fund that earned a 9% profit and y represent the amount invested in the mutual fund that earned a 2% profit. Given that the total investment is $1,400, we can express this as an equation x + y = 1400. Additionally, the profits from these investments must add up to $49, which gives us a second equation, 0.09x + 0.02y = 49.

To find the amounts invested in each fund, we can solve this system of equations with the following steps:

1. Express y in terms of x from the first equation: y = 1400 - x.
2. Substitute y in the second equation: 0.09x + 0.02(1400 - x) = 49.
3. Simplify the second equation and solve for x.
4. Substitute the value of x into y = 1400 - x to find y.

This step-by-step process will give you the amounts invested in each mutual fund.