A retired woman has $100,000 to invest. She wants to invest in two funds: one with a 9% annual yield and another with a 13% annual yield. The goal is to earn $10,000 per year. We need to find out how much she should invest in each fund.

1. Problem Description

A retired woman has $100,000 to invest. She wants to invest in two funds: one with a 9$10,000 per year. We need to find out how much she should invest in each fund.

2. Solution Steps

Let $x$ be the amount invested in the 9% fund, and $y$ be the amount invested in the 13% fund. We can set up two equations based on the given information:

Equation 1 (Total Investment): $x + y = 100000$

Equation 2 (Total Income): $0.09x + 0.13y = 10000$

We can solve this system of equations. First, solve Equation 1 for $x$:

$x = 100000 - y$

Substitute this expression for $x$ into Equation 2:

$0.09(100000 - y) + 0.13y = 10000$

$9000 - 0.09y + 0.13y = 10000$

$0.04y = 10000 - 9000$

$0.04y = 1000$

$y = \frac{1000}{0.04}$

$y = 25000$

Now, substitute the value of $y$ back into the equation for $x$:

$x = 100000 - 25000$

$x = 75000$

So, the woman should invest $75,000 in the 9$25,000 in the 13% fund.

3. Final Answer

The woman should invest $75,000 in the 9$25,000 in the 13% fund.