5 coffee and 4 tea cost rupees 96, 5 milk and 6 coffee cost rupees 32, and 7…

Concept: When several linear relationships share the same set of unknowns and their coefficients for each unknown add up to the same common number across the relationships, adding all the relationships together eliminates the need to solve for each unknown separately — the sum directly gives that common number times the total of the unknowns.

Application: Applying this to the given prices — let C, T, and M denote the price of one coffee, one tea, and one milk respectively:

1. Translate the three statements into equations: 5C + 4T = 96; 5M + 6C = 32; 7T + 6M = 37.

2. Add all three equations term by term: (5C + 6C) + (4T + 7T) + (5M + 6M) = 96 + 32 + 37, which gives 11C + 11T + 11M = 165.

3. Factor out the common coefficient 11: 11(C + T + M) = 165.

4. Divide both sides by 11: C + T + M = 165 / 11 = 15.

Cross-check: 11 x 15 = 165, and independently, 96 + 32 + 37 = 165 as well — the two computations agree, confirming the result.

Therefore, the combined price of 1 tea, 1 coffee, and 1 milk is 15.