Two institutions decided to award their employees for resourcefulness, competence and determination in the form of prizes at the rate of Rs. x, Rs. y, Rs. z respectively per person. The first institution decided to award respectively 4, 3 and 2 employees with total prize money Rs. 37,000 and second institution decided to award respectively 5, 3 and 4 employees with the total prize money of Rs. 47,000 for resourcefulness, competence and determination. All the prizes per person together amount to Rs. 12,000.
The linear equations representing the above information are
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4x + 3y + 2z = 37000, 5x + 3y + 4z = 47000, x + y + z = 12000
Each total is (number of employees) × (prize per person), added over the three qualities.
First institution: 4 prizes of Rs. x, 3 of Rs. y and 2 of Rs. z make Rs. 37,000:
\(4x + 3y + 2z = 37000\)
Second institution: 5 prizes of Rs. x, 3 of Rs. y and 4 of Rs. z make Rs. 47,000:
\(5x + 3y + 4z = 47000\)
One prize of each kind together comes to Rs. 12,000:
\(x + y + z = 12000\)