A retired woman has $120,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another riskier fund that has a 13% annual yield. How much should she invest in each fund if she would like to earn $12,000 per year from her investments?

She should invest $90,000 in the safe fund and $30,000 in the riskier fund

Step-by-step explanation:

* Lets explain how to solve the problem

- A retired woman has $120,000 to investment

- She has two options:

# Save investment fund that has an annual yield of 9%

# Riskier fund that has a 13% annual yield

- She would like to earn $12,000 per year from her investments

* Assume that she invest $x in the safe fund and $y in the riskier fund

∵ The total investment is $120,000

∵ x represents the amount of money invested in the safe fund

∵ y represents the amount of money invested in the riskier fund

∴ x + y = 120,000 ⇒ (1)

∵ The interest I = Prt, where P is the invested amount, r is the

percentage of the interest per year in decimal, t is the time

∵ The interest of x amount is 9%

∴ I = x * 9/100 * 1 = 0.09 x

∴ The interest of y amount is 13%

∴ I = y * 13/100 * 1 = 0.13 u

∵ She would like to earn $12,000 per year from her investment

∴ 0.09 x + 0.13 y = 12,000 ⇒ (2)

* Lets solve the two equations to find x and y

- Multiply equation (1) by - 0.13 to eliminate y

∵ - 0.13 x + - 0.13 y = - 15600 ⇒ (3)

- Add equations (2) and (3)

∴ (0.09 x + - 0.13 x) + (0.013 y + - 0.13 y) = 12,000 + - 15,600

∴ - 0.04 x = - 3,600

- Divide both sides by - 0.04

∴ x = 90,000

- Substitute the value of x in equation (1)

∴ 90,000 + y = 120,000

- Subtract 90,000 from both sides

∴ y = 30,000

∵ x represents the amount invested in the safe fund

∵ y represents the amount invested in the riskier fund

∴ She should invest $90,000 in the safe fund and $30,000 in

the riskier fund