Question

Two schools P and Q want to award their selected students on the values of Tolerance, Kindness and Leadership. The school P wants to award Rs. x each, Rs. y each and Rs. z each for the three respective values to 3, 2 and 1 students respectively with a total award money of Rs. 2,200. School Q wants to spend Rs. 3,100 to award its 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each value is Rs. 1,200, using matrices, find the award money for each value. Apart from these three values, suggest one more value that should be considered for award.

Answer 1

According to question, 

3x + 2y + z = 2200 

4x + y + 3z = 3100 

x + y + z = 1200 

The above system of equation may be written in matrix form as AX = B

Now, A₁₁ = (1 – 3) = –2, 

A₁₂ = – (4 – 3) = –1, 

A₁₃ = (4 – 1) = 3, 

A₂₁ = – (2 – 1) = –1, 

A₂₂ = (3 – 1) = 2, 

A₂₃ = – (3 – 2) = –1 

A₃₁ = (6 – 1) = 5, 

A₃₂ = – (9 – 4) = –5, 

A₃₃ = (3 – 8) = –5

i.e., Rs. 300 for tolerance, Rs. 400 for kindness and Rs. 500 for leadership are awarded.

One more value like punctuality, honesty etc may be awarded.