Amila, Babu and Christy earn a total of Rs. 970 per week as the take home salary. Amila's take home salary plus twice each of the other's is Rs. 1640. Christy's take-home salary plus twice each of the other's is Rs.
1600. Using the matrices, find the take home salary of each.

Let the take-home salaries of Amila, Babu, and Christy be denoted by \( A \), \( B \), and \( C \) respectively.

### System of Equations:
We can translate the given information into the following system of equations:

1. The total salary:
\[
A + B + C = 970
\]

2. Amila's salary plus twice each of the others:
\[
A + 2B + 2C = 1640
\]

3. Christy's salary plus twice each of the others:
\[
C + 2A + 2B = 1600
\]

### Step 1: Matrix Representation
We can represent this system of equations as a matrix equation \( AX = B \), where:

\[
\begin{pmatrix}
1 & 1 & 1 \\
1 & 2 & 2 \\
2 & 2 & 1
\end{pmatrix}
\begin{pmatrix}
A \\
B \\
C
\end{pmatrix}
=
\begin{pmatrix}
970 \\
1640 \\
1600
\end{pmatrix}
\]

### Step 2: Solving the Matrix Equation

Now, we will solve this system of equations using the matrix method. I'll calculate the solution.

Amila, Babu and Christy earn a total of Rs. 970 per week as the take-home salary. Amila's take-home salary plus twice each of the other's is Rs. 1640. Christy's take-home salary plus twice each of the other's is Rs. 1600. Using the matrices, find the take-home salary of each.

Learn how to find the take-home salaries of Amila, Babu, and Christy using matrix algebra. This problem involves setting up and solving a system of linear equations using matrix methods, suitable for students in Grades 9-12.

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