Question

Robert has $20,000, part or all of which he wants to invest into a combination of government bonds and municipal bonds. he wants to invest no more than $5,000 into municipal bonds, and at least twice as much into government bonds than into municipal bonds. let x be the amount invested into government bonds, and let y be the amount invested into municipal bonds. which system of inequalities describes robert’s investment options?

a. x ≥ 2y and y ≤ 5000
b. x ≤ 2y and y ≥ 5000
c. x ≥ 5000 and y ≤ 2x
d. x ≤ 5000 and y ≥ 2x

Answer 1

Robert's investment options are described by the inequalities x ≥ 2y (at least twice as much into government bonds as into municipal bonds) and y ≤ 5000 (no more than $5,000 into municipal bonds), which corresponds to option (a). x ≥ 2y and y ≤ 5000.

Step-by-step explanation:

The system of inequalities that describes Robert's investment options is represented by two conditions based on the information provided:
1. He wants to invest at least twice as much into government bonds than into municipal bonds.
2. He wants to invest no more than $5,000 into municipal bonds.
Letting x be the amount invested into government bonds, and y be the amount invested into municipal bonds, the system of inequalities can be written as:

• x ≥ 2y (at least twice as much into government bonds as into municipal bonds)
• y ≤ 5000 (no more than $5,000 into municipal bonds)

This corresponds to option (a): x ≥ 2y and y ≤ 5000.