SOLUTION: the sum of three numbers is 16. one of the numbers is the sum of the other numbers. it is also four times the difference between the other two numbers. what are the three numbers?

Question 373495: the sum of three numbers is 16. one of the numbers is the sum of the other numbers. it is also four times the difference between the other two numbers. what are the three numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the sum of three numbers is 16.
x + y + z = 16
:
one of the numbers is the sum of the other numbers.
x = y + z
0 = -x + y + z
:
it is also four times the difference between the other two numbers.
x = 4(y-z)
:
what are the three numbers?
:
Use elimination on the 1st and 2nd equations
x + y + z = 16
-x +y + z = 0
----------------subtraction eliminates y and z find x:
2x = 16
x = 8
:
Replace x with 8 in the 2nd equation
8 = 4(y-z)
Divide both sides by 4
2 = y - z
z = y - 2
:
Back to the 1st equation
x + y + z = 16
8 + y + (y-2) = 16
2y - 2 = 16 - 8
2y = 8 + 2
2y = 10
y = 5
Obviously then,
z = 3
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