A person with no more than $15,000 to invest plans to place the money in two investments. One investment is high-risk, high yield; the other is low risk, low yield. At least $2,000 is to be placed in the high-risk investment. Furthermore, the amount invested at low risk should be at least three times the amount invested at high-risk. Find a system of inequalities that describes all possibilities for placing the money in the high- and low-risk investments.
let x be high risk investment
and y be low risk investment
so x + y < 15000
y>3x
x> 2000
To find the system of inequalities that describes all possibilities for placing the money in the high-risk and low-risk investments, we need to consider the given conditions:
1. At least $2,000 is to be placed in the high-risk investment.
2. The amount invested at low risk should be at least three times the amount invested at high-risk.
3. The total investment should not exceed $15,000.
Let's denote the amount invested in the high-risk investment as "x" (in dollars) and the amount invested in the low-risk investment as "y" (in dollars).
Based on the given conditions, we have:
1. x ≥ 2000 (At least $2,000 needs to be placed in the high-risk investment).
2. y ≥ 3x (The amount invested at low risk should be at least three times the amount invested at high-risk).
3. x + y ≤ 15000 (The total investment should not exceed $15,000).
Therefore, the system of inequalities that describes all possibilities for placing the money in the high-risk and low-risk investments is:
x ≥ 2000
y ≥ 3x
x + y ≤ 15000