Question

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. 

Answer 1

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

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.