At a canteen, 2 teas, 1 coffee and 1 juice cost ₹75; 1 tea, 2 coffees and 1 juice cost ₹85; and 1 tea, 1 coffee and 2 juices cost ₹100. Using the matrix method, what does one juice cost?

Explanation

1. 01

   $A = \begin{bmatrix}2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2\end{bmatrix}$, $|A| = 4$ and $\operatorname{adj} A = \begin{bmatrix}3 & -1 & -1 \\ -1 & 3 & -1 \\ -1 & -1 & 3\end{bmatrix}$.

2. 02

   $X = \frac{1}{4}\begin{bmatrix}3 & -1 & -1 \\ -1 & 3 & -1 \\ -1 & -1 & 3\end{bmatrix}\begin{bmatrix} 75 \\ 85 \\ 100 \end{bmatrix} = \begin{bmatrix}10 \\ 20 \\ 35\end{bmatrix}$.

3. 03

   Tea ₹10, coffee ₹20, juice ₹35. Check: $10 + 20 + 2(35) = 100$.