One safe investment pays 2% per year, and a more risky investment pays 15% per year. a woman who has $144,000 to invest would like to have an income of $10,940 per year from her investments. how much should she invest at each rate?

Given: 

x - investment rate at 2% per year
y - investment rate at 15% per year
Income per year = $10,940
Investment = $144,000

Solution:

Since the summation of each investment rate is equal to the investment, then we can create an equation which is:

x + y = $144,000

Now, we have two unknowns thus; we need another equation to solve the problem. The other equation can be created by simply equating the total income per year to the sum of the portions of the investments at each rate. The equation can be written as:

0.02x + 0.15y = $10,940

Now that we have two equations, we recall the equations.

x + y = $144,000
0.02x + 0.15y = $10,940

To solve for the unknowns, we substitute the 1st equation to the other.

x + y = $144,000
x = $144,000 - y

substituting,

0.02($144,000 - y) + 0.15y = $10,940

y = $62,000

calculating x,

x = $144,000 - y

x = $144,000 - $62000

x = $82,000