Answer :

Let the numbers are x, y,z be the prize amount per person for adaptability, carefulness and calmness respectively


As per the given data we get,


2x + 4y + 3z = 29000


5x + 2y + 3z = 30500


X + y + z = 9500


These three equations can be written as



A X = B


|A| = 2(2 – 3) – 4(5 – 3) + 3(5 – 2)


= 2(– 1) – 4(2) + 3(3)


= – 2 – 8 + 9


= – 1


Hence, the unique solution given by x = A – 1B


C11 = (– 1)1 + 1 (2 – 3) = – 1


C12 = (– 1)1 + 2 (5 – 3) = – 2


C13 = (– 1)1 + 3 (5 – 2) = 3


C21 = (– 1)2 + 1 (4 – 3) = – 1


C22 = (– 1)2 + 2 (2 – 3) = – 1


C23 = (– 1)2 + 3 (2 – 4 ) = – 2


C31 = (– 1)3 + 1 (12 – 6) = 6


C32 = (– 1)3 + 2 (6 – 15) = – 9


C33 = (– 1)3 + 3 (4 – 20) = – 16


Adj A =


X = A – 1 B =


X =


X =


X =


=


Hence, x = 2500, y = 3000 and z = 4000


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