Model the problem using a system of linear equations. Then solve using the augmented matrix. Suppose $24,000 is invested in three different accounts paying 3%, 4%, and 7%
Annual interest. The interest earned after 1 year is $1270, and the amount
Invested at 7% is equal to the sum of the amounts invested at 3% and 4%.
Find the amount invested at 3%.
A) $5000
B) $6000
C) $7000
D) $8000

Question

Quizplus · Accepted Answer

The system of equations based on the problem statement is:1. $x + y + z = 24000$ (total investment)2. $0.03x + 0.04y + 0.07z = 1270$ (total interest)3. $z = x + y$ (amount at 7% equals sum of amounts at 3% and 4%)Solving this system using an augmented matrix and applying row operations leads to finding $x = 5000$, which is the amount invested at 3%.

Model the Problem Using a System of Linear Equations