SOLUTION: the sum of three number is 55. the difference of the largest and the smallest is 51, and the sum of the two smaller number is 12. find the numbers.

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Question 994015: the sum of three number is 55. the difference of the largest and the smallest is 51, and the sum of the two smaller number is 12. find the numbers.
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
x + y + z = 55,    (1)

x     - z = 51,    (2)

    y + z = 12.    (3)


where x is the largest number and z is the smallest one. 


Now, distract (3) from (1). You will get x = 55 - 12 = 43.


Substitute it into (2), and you will find z = 43 - 51 = -8.


Substitute z = -8 into (3), and you will find y = 12 + 8 = 20.


Answer. x = 43, y = 20, z= -8.