Megan has at most $1500 to invest. She plans to invest some of the money in a long-term CD at 6% and some of it in a short-term CD at 3%. She wants to earn at least $75 in interest per year. Write a system of inequlites to represent the situation, and use it to find all of the combinations of investments that Megan can make with there two CD's.

Question

Megan has at most $1500 to invest. She plans to invest some of the money in a long-term CD at 6% and some of it in a short-term CD at 3%. She wants to earn at least $75 in interest per year. Write a system of inequlites to represent the situation, and use it to find all of the combinations of investments that Megan can make with there two CD's.

1) Define the varibles
2)Develope the inequality that satisfies each condition below.
a. Total money invested.
b. Amount of money invested in each CD.

Answer 1

1) Let's define:

x = amount of money invested in the long-term CD (in dollars)
y = amount of money invested in the short-term CD (in dollars)

2) Now let's develop the inequalities that satisfy each condition:
a. Total money invested:
The total amount of money Megan invests is given as $1500. Therefore, the inequality is:
x + y ≤ 1500

b. Amount of money invested in each CD:
The amount of money invested in the long-term CD should be greater than or equal to $0, and the amount of money invested in the short-term CD should also be greater than or equal to $0. Therefore, the inequalities are:
x ≥ 0
y ≥ 0

3) Interest earned:
Megan wants to earn at least $75 in interest per year. The interest earned on the long-term CD at 6% is 0.06x, and the interest earned on the short-term CD at 3% is 0.03y. Therefore, the inequality is:
0.06x + 0.03y ≥ 75

Now that we have defined the variables and developed the inequalities, we can solve the system of inequalities to find all the combinations of investments Megan can make with the two CDs.