SOLUTION: The sum of three numbers is 100. The second number is 2 more than three times the first number, and the third number is the sum of the first two numbers. What are the numbers?

Question 247106: The sum of three numbers is 100. The second number is 2 more than three times the first number, and the third number is the sum of the first two numbers. What are the numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of three numbers is 100.
x + y + z = 100
:
The second number is 2 more than three times the first number,
y = (3x + 2)
:
the third number is the sum of the first two numbers.
z = (x + y)
:
What are the numbers?
:
From the 2nd equation, replace y with (3x+2) in the 3rd equation
z = x + (3x+2)
z = (4x + 2)
:
Replace y and z in the 1st equation
x + (3x+2) + (4x+2) = 100
8x + 4 = 100
8x = 100 - 4
8x = 96
x = 12
then
z = 4x + 2
z = 4(12) + 2
z = 50
and
y = 3x + 2
y = 3(12) + 2
y = 38
:
:
Is this true?
12 + 38 + 50 = 100
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