Question

An investor invested a total of $1,400 in two mutual funds. One find earned a 7% profit while the other earned a 4% profit. If the investors total profit was $89, how much was invested in each mutual fund?

Answer 1

It was invested $1,100 in the first one and $300 in the second one.

Explanation:

To solve this situation use a linear system of equations.

Given that the total invested in two mutual funds is $1,400.

Let x be the amount invested in the first one

Let y be the amount invested in the second one.

`x+y=1400\text{ (1)}`

If one find earned a 7% profit and the second one earned a 4% profit. If the investors' total profit was $89.

`0.07x+0.04y=89\text{ (2)}`

Now, that we have the system of equations with two equations and two variables. Use the substitution method to solve it, isolate one of the variables in equation (1) and plug it into equation (2):

`y=1400-x\text{ (1)}`

Plug it into (2)

`\begin{gathered} 0.07x+0.04(1400-x)=89 \\ 0.07x+56-0.04x=89 \\ \text{0}.03x=89-56 \\ \text{0}.03x=33 \\ x=(33)/(0.03) \\ x=\text{ \$1,100} \end{gathered}`

In the first fund, it was invested $1,100.

Now, substitute x=1,100 into equation (1), solve for y.

`\begin{gathered} y=1400-x \\ y=1400-1100 \\ y=\text{ \$300} \end{gathered}`

In the second fund, it was invested $300.