# 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(12660)   (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(6287)   (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