A trust fund has $200,000 to invest. Three

ahmed zubair

ahmed zubair

Answered question

2022-09-14

A trust fund has $200,000 to invest. Three alternative investments have been identified, earning income of 10 percent, 7 percent and 8 percent respectively. A goal has been set to earn an annual income of $16,000 on the total investment. One condition set by the trust is that the combine investment in alternatives 2 and 3 should be triple the amount invested in alternative 1. Determine the amount of money, which should be invested in each option to satisfy the requirements of the trust fund. Solve by Gauss- Jordon method

 

What are the equations formed in this question?

Answer & Explanation

karton

karton

Expert2023-06-03Added 613 answers

To solve this problem using the Gauss-Jordan method, we need to set up a system of equations based on the given conditions.
We need denote the amount invested in alternative 1 as x, the amount invested in alternative 2 as y, and the amount invested in alternative 3 as z.
Based on the information given, we can establish the following equations:
1. The total investment amount: x+y+z=200,000.
2. The income earned from each investment:
- Income from alternative 1: 0.10x.
- Income from alternative 2: 0.07y.
- Income from alternative 3: 0.08z.
The total income earned from the investments should be 16,000, so we have the equation: 0.10x+0.07y+0.08z=16,000.
3. The condition set by the trust fund: The combined investment in alternatives 2 and 3 should be triple the amount invested in alternative 1. Mathematically, this can be expressed as y+z=3x.
Therefore, the system of equations can be written as:
x+y+z=200,000
0.10x+0.07y+0.08z=16,000
y+z=3x
We can now solve this system of equations using the Gauss-Jordan method to find the values of x, y, and z that satisfy the requirements of the trust fund.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?