SOLUTION: The sum of three numbers is 9. The first number minus the second plus the third is 3. The first minus the third is 1 more than the second. Find the numbers. What is the first nu

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Question 230976: The sum of three numbers is 9. The first number minus the second plus the third is 3. The first minus the third is 1 more than the second. Find the numbers.
What is the first number? _____
What is the second number? ______
What is the third number? ______
Found 2 solutions by ankor@dixie-net.com, stanbon:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Three integers, x, y, z
:
Write an equation for each statement:
:
The sum of three numbers is 9.
x + y + z = 9
:
The first number minus the second plus the third is 3.
x - y + z = 3
:
The first minus the third is 1 more than the second.
x - z = y + 1
rearrange to:
x - y - z = 1
:
Add to the 1st equation
x + y + z = 9
x - y - z = 1
----------------addition eliminates y and z, find x
2x = 10
x = 5
:
Substitute for x and add the 1st two equations
5 + y + z = 9 >>>> y + z = 9 - 5 >>>> y + z = 4
5 - y + z = 3 >>>>-y + z = 3 - 5 >>>>-y + z =-2
................................................--------------------
...................................................................2z = 2
z = 1
:
I'll let you find y

Find the numbers.
What is the first number? _____
What is the second number? ______
What is the third number? ______

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The sum of three numbers is 9. The first number minus the second plus the third is 3. The first minus the third is 1 more than the second. Find the numbers.
---------------------
Equations:
a + b + c = 9
a - b + c = 3
a + 0 - c = b+1
---------------------
Rearrange:
a + b + c = 9
a - b + c = 3
a - b - c = 1
---------------------
Use any method to solve the system to get:
a = 5
b = 3
c = 1
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Cheers,
stan H.