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.