SOLUTION: The sum of three numbers is 147. The second number is 4 more than two times the first number. The third number is five less than three times the first number. Find the three number

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Question 214880: The sum of three numbers is 147. The second number is 4 more than two times the first number. The third number is five less than three times the first number. Find the three numbers.
Please help me solve this problem. I tried to do it a few times but I get confused right off the bat. Thanks for any help!
Found 2 solutions by josmiceli, checkley77:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be a, b, and c
given:
(1) a+%2B+b+%2B+c+=+147
(2) b+=+2a+%2B+4
(3) c+=+3a+-+5
I can substitute (2) and (3) into (1)
(1) a+%2B+b+%2B+c+=+147
a+%2B+2a+%2B+4+%2B+3a+-+5+=+147
6a+-+1+=+147
6a+=+148
a+=+74%2F3
This isn't a whole number. Are you sure you copied
the problem right?

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
X+Y+Z=147
Y=2X+4
Z=3X-5
X+(2X+4)+(3X-5)=147
6X-1=147
6X=147+1
6X=148
X=148/6
X=24 2/3 ANS. ANS
Y=2*24 2/3+4=49/3+4=53 1/3 ANS
Z=3*24 2/3-5=74-5=69 ANS.
PROOF:
24 2/3+53 1/3+69=147
147=147