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 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) (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) (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
RELATED QUESTIONS
The sum of three numbers is 100. The second number is 2 more than three times the first... (answered by ankor@dixie-net.com)
Th second of the three numbers is 2 more than the first. The third number is twice the... (answered by ankor@dixie-net.com)
The sum of three numbers is 79 the second number is 9 times the first and the third... (answered by ewatrrr)
Using Equations to solve Problems. The sum of 3 numbers is 39. The second number is... (answered by bucky)
The sum of three numbers is 74. The first number is 10 more than the third. The second... (answered by josgarithmetic)
The sum of three numbers is 93 . The second number is 2 times the third. The first (answered by Alan3354,josgarithmetic)
The sum of three numbers is 74 . The first number is 10 more than the second . The third... (answered by rfer)
The sum of three numbers is 62 . The first number is 10 more than the second . The third (answered by algebrahouse.com)
The sum of three numbers is 74 . The second number is 6 more than the first. The third (answered by Alan3354)