# math

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: thfe other is low risk, low yield. at least \$2,000 is to be plaaced in the high-risk investment. furthermore, thfe amount invested at low risk should be at least three times the amounted invested at high risk. find and graph a system of inequalities that describes all possibilities for plaacing the money in the high-and low risks investments

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1. Let H be the amount of investments for high risk products, and
L be the amount for low-risk products.

"with no more than \$15,000 to invest "
H+L≤15000

"at least \$2,000 is to be plaaced in the high-risk investment"
H≥2000

"amount invested at low risk should be at least three times the amount invested at high risk"
L≥3H

Draw a graph with H in the x-axis, and L in the y-axis (or vice versa).
Represent the above inequalities on the graph.
Shade the impossible regions. The unshaded region in the resulting graph represents the possible investment options.

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2. A person with no more than ​\$16000 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 ​\$1000 is to be placed in the​ high-risk investment.​ Also, the amount invested at low risk should be at least 2 times the amount invested at high risk. Find and graph a system of inequalities.

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