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:

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.