SOLUTION: The sum of three numbers is 6. The third number is the sum of the first and second number. The first number is one more than the third number. Find the numbers.

Question 14061: The sum of three numbers is 6. The
third number is the sum of the first
and second number. The first number
is one more than the third number.
Find the numbers.
Found 2 solutions by rahman, bam878s:
Answer by rahman(247) (Show Source): You can put this solution on YOUR website!
Suppose:
x is the first number
y is the second number
z is the third number
We can construct mathematic model from the problem:
x + y + z = 6
z=x+y
x=z+1
Look the first equation and the second equation:
x+y+z=6
(x+y)+z=6
z+z=6
2z=6

z=3
Substitute z=3 to x = z+1
x = z+1
x = 3+1
x=4
Substitute x=4 and z=3 to z=x+y
z=x+y
3=4+y
3-4=y
y=-1
Thus, the first number is 4, the second number is -1, and the third number is 3
OK
Answer by bam878s(77) (Show Source): You can put this solution on YOUR website!
let x = third number
y = first number
z = second number
We know x+y+z=6
also x = y+z (1).
and y = x+1 (2).
plug y back into equation (1) to get x = (x+1) + z.
Now subtract x from both sides of this equation to get
0=1+z.
Now subtract 1 from both sides to get
-1=z.
Now we know x=y+(-1), x+y+(-1)=6.
plug x into this equation to get
(y+(-1)) + y + (-1) = 6
solve for y.
we have,
y-1+y-1=6
2y-2=6
add 2 to both sides to get
2y=8
now divide by 2 to get
y=4
Now that we know z and y we can use equation (1) to find x.
x=4+(-1)= 3.
Hope this helps
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