Two institutions decided to award their employees for resourcefulness competence and determination in the form of prizes at the rate of ₹x, ₹y, ₹z respectively per person. The first institution decided to award respectively 4. 3 and 2 employees with total prize money ₹37.000 and second institution decided to award respectively 5, 3 and 4 employees with the total prize money of ₹47.000 for resourcefulness, competence and determination. All the prizes per person together amount ₹12.000.

The linear equations representing the above information are

4x + 3y + 2z = 37000

5x + 3y + 4z = 47000

x + y + z = 12000