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?

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Question 557050: 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?
Found 2 solutions by rfer, Earlsdon:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
x+3x+2+4x+2=100
8x=96
x=96/8
x=12
3x+2=38
4x+2=50

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the three numbers be: a, b, and c.
b = 3a+2 "The second number is 2 more than 3 times the first number."
c = a+b "The third number is the sum of the first two numbers."
a+b+c = 100 "The sum of three numbers is 100." Substitute b = 3a+2.
a+(3a+2)+c = 100 Substitute c = a+b and b = 3a+2.
a+(3a+2)+a+3a+2 = 100 Simplify.
8a+4 = 100 Subtract 4 from both sides.
8a = 96 Divide both sides by 8.
a = 12
b = 3(12)+2
b = 38
c = 12+38
c = 50
Check:
a+b+c = 12+38+50 = 100