Q. 355.0( 3 Votes )

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award ₹x each ₹y each and ₹ z each for the three respective values to 3, 2 and 1 students respectively with total award money of ₹16,00. School B wants to Spend ₹2,300 to award its 4,1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is ₹900, using matrices, find the award money for each value, Apart from these three values, suggest one more value which should be considered for the award.

Answer :

Let the numbers are x, y,z be the prize amount per person for sincerity, truthfulness and helpfulness respectively


As per the given data we get,


3x + 2y + z = 1600


4x + y + 3z = 2300


x + y + z = 900


These three equations can be written as



A X = B


|A| = 3(1 – 3) – 2(4 – 3) + 1(4 – 1)


= 3(– 2) – 2(1) + 1(3)


= – 6 – 2 + 3


= – 5


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


C11 = (– 1)1 + 1 (1 – 3) = – 2


C12 = (– 1)1 + 2 (4 – 3) = – 1


C13 = (– 1)1 + 3 (4 – 1) = 3


C21 = (– 1)2 + 1 (2 – 1) = – 1


C22 = (– 1)2 + 2 (3 – 1) = 2


C23 = (– 1)2 + 3 (3 – 2 ) = – 1


C31 = (– 1)3 + 1 (6 – 1) = 5


C32 = (– 1)3 + 2 (9 – 4) = – 5


C33 = (– 1)3 + 3 (3 – 8) = – 5


Adj A =


X = A – 1 B =


X =


X =


X =


=


Hence, x = 200, y = 300 and z = 400


Excellence in extra curricular activities should be another value considered for an award.

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