Question

An investor invests in stock at 5% and in bonds at 8% in order to maintain an

income of at least $20,000. Write the linear inequality that expresses the
relationship between the amounts invested in stocks and bonds.

Answer 1

Let's say X is the amount you invest in stock, and B is the amount you invest in bonds.

How much income will your stocks generate in a year? They will generate X * 0.05

How much income will your bonds generate in a year? They will generate B * 0.08

And you need the sum of these two amounts to be greater than or equal to 20,000

So your equation is:

X*0.05 + B*0.08 >= 20,000

This is the correct answer, but just in case your teacher is looking for X in terms of B, just move the B term to the other side of the equation:

X*0.05 >= 20,000 - B*0.08

and divide both sides by 0.05:

X >= 400,000 - B*1.6