The Solution

The conventional method: let the price of an apple, a pear and a mango in Rupees be a, p and m respectively.

5a + 3p = 19           …       …       (1)

3a + 4m = 10          …       …       (2)

2p + 3m = 9            …       …       (3)

3 x (1) – 5 x (2) gives:

9p – 20 m = 7         …       …       (4)

9 x(3) – 2 x(4) gives 67m = 67 or m = 1

Substituting in (4), p = 3.

 
Substituting in (1), a = 2.

Thus a = 2, p = 3 and m = 1.

Therefore 8a + 5p + 7m = 38.

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