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 ₹ 1,600. 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 award.

HINT: By the given data, we have




Let the amount x, y and z be considered for sincerity, truthfulness and helpfulness.


According to the questions,


3x + 2y + z = 1600


4x + y + 3z = 2300


X + y + z = 900


Converting into the matrix form


AX = B



R1 – 3R3


R2 – 4R3



2R2 - R1



Converting back into the equations we get


- y - 2z = - 1100


- 5y = - 1500


X + y + z = 900


Y = 300


- 300 - 2z = - 1100


- 2z = - 800


Z = 400


X + 300 + 400 = 900


X = 900 - 700


X = 200


₹ 200 for sincerity, ₹ 300 for truthfulness and ₹ 400 for helpfulness. One more value may be like honesty, kindness, etc.


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