SOLUTION: I'm having trouble with this question: The mean of three numbers is 31. The second is 1 more than twice the first. The third is 4 less than 3 times the first. Find the numbers.

Question 959420: I'm having trouble with this question: The mean of three numbers is 31. The second is 1 more than twice the first. The third is 4 less than 3 times the first. Find the numbers.
I put the equation x+2x+1+3x-4
The problem is that I don't know what to equal it to. I tried with 31, as that is the mean, but I checked it and it did not work. Can you please help me? Thank you.
Found 3 solutions by rothauserc, MathLover1, lwsshak3:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
(x +2x+1 +3x-4) / 3 = 31
here we have used the definition of the mean
(x +2x+1 +3x-4 = 93
multiply both sides of = by 3
6x -3 = 93
6x = 96
x = 16
the numbers are 16, 33, 44
note that (16 +33 +44) / 3 = 31

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

The mean of three numbers is .

if the second is more than twice the first, we have

if the third is less than times the first, we have

substitute it in
........solve for

now find and

Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
'm having trouble with this question: The mean of three numbers is 31. The second is 1 more than twice the first. The third is 4 less than 3 times the first. Find the numbers.
***
let x=1st number
2x+1=2nd number
3x-4=3rd number
..
(x+2x+1+3x-4)/3=31 (average of 3 numbers=31)
6x-3=93
6x=96
x=16
2x+1=33
3x-4=44
numbers are: 16, 33, and 44
note:"mean" just means average in this case
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