Respuesta :
Using a system of equations, the amounts invested in each fund are given as follows:
- Growth: $2,000.
- Income: $2,000.
- Market: $2,000.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
- Variable x: amount invested into the growth fund.
- Variable y: amount invested into the income fund.
- Variable z: amount invested into the market fund.
The teacher invested 5000, hence:
x + y + z = 5000.
After a year, the amount was of $5,450, hence, considering the return rates:
1.12x + 1.08y + 1.05z = 5450.
The teacher invested twice as much in the income fund as in the money market fund, hence:
y = 2z.
Then, replacing y = 2z in the first two equations:
- x + 3z = 5000 -> x = 5000 - 3z.
- 1.12x + 3.21z = 5450.
Replacing the first equation into the second.
1.12(5000 - 3z) + 3.21z = 5450.
0.15z = 150
z = 150/0.15
z = 1000.
Hence:
- y = 2z = 2000.
- x = 5000 - 3z = 2000.
The amounts invested in each fund are given as follows:
- Growth: $2,000.
- Income: $2,000.
- Market: $2,000.
More can be learned about a system of equations at https://brainly.com/question/24342899
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