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Janie had just won a prize money worth GHS 100,000 and would like to invest it for a rainy day. In order to reduce the level of risk on her investments, she has been advised to diversify her investments. She has the option of investing in three different assets – Asset 1 which yields an interest of 10% annum, Asset 2 which yields an interest of 12% per annum and Asset 3 which yields an interest of 8% per annum. Due to the high risk nature of Assets 1 and 2, Janie is advised to invest not more than 60% of the total amount of the money in Assets 1 and 2. Janie would want to ensure that she earns returns that will be at exactly 6% of her investment. Formulate the mathematical equations or inequalities that will afford the chance Janie to meet her requirements.

Question

Janie had just won a prize money worth GHS 100,000 and would like to invest it for a rainy day. In order to reduce the level of risk on her investments, she has been advised to diversify her investments. She has the option of investing in three different assets – Asset 1 which yields an interest of 10% annum, Asset 2 which yields an interest of 12% per annum and Asset 3 which yields an interest of 8% per annum. Due to the high risk nature of Assets 1 and 2, Janie is advised to invest not more than 60% of the total amount of the money in Assets 1 and 2. Janie would want to ensure that she earns returns that will be at exactly 6% of her investment. Formulate the mathematical equations or inequalities that will afford the chance Janie to meet her requirements.

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Solution 1

Let's denote the amount of money Janie invests in Asset 1, Asset 2, and Asset 3 as x, y, and z respectively.

From the problem, we have the following conditions:

  1. The total amount of money invested should be equal to the prize money: x + y + z = GHS 100,000

  2. Due to the high risk nature of Assets 1 and 2, Janie is advised to invest not more than 60% of the total amount of the money in Assets 1 and 2: x + y ≤ 0.60 * 100,000 = GHS 60,000

  3. Janie wants to ensure that she earns returns that will be exactly 6% of her investment. This means the sum of the returns from each asset should be equal to 6% of the total investment: 0.10x + 0.12y + 0.08z = 0.06 * 100,000 = GHS 6,000

These are the mathematical equations and inequalities that represent Janie's investment strategy.

This problem has been solved

Solution 2

Let's denote the amount of money Janie invests in Asset 1, Asset 2, and Asset 3 as x, y, and z respectively.

From the problem, we have the following conditions:

  1. The total amount of money invested should be equal to the prize money: x + y + z = 100,000

  2. Due to the high risk nature of Assets 1 and 2, Janie is advised to invest not more than 60% of the total amount of the money in Assets 1 and 2: x + y ≤ 0.60 * 100,000 = 60,000

  3. Janie wants to ensure that she earns returns that will be at exactly 6% of her investment. The total interest from the three assets should be 6% of the total investment: 0.10x + 0.12y + 0.08z = 0.06 * 100,000 = 6,000

These are the mathematical equations and inequalities that represent Janie's investment problem.

This problem has been solved

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