Question

The sum of three numbers is 3. if the second number is subtracted from the sum of the first and third numbers, the result is 9. if the third number is subtracted from the sum of the first and second numbers, the result is -5. find the three numbers.

Answer 1

To solve this problem, we can assign variables to the three numbers and create a system of equations. By solving this system, we can find the values of the three numbers. The three numbers are -6, -4, and 11.

Step-by-step explanation:

To solve this problem, we can assign variables to the three numbers. Let's call the first number 'a', the second number 'b', and the third number 'c'. We are given the following information:

Now we can solve this system of equations to find the values of 'a', 'b', and 'c'. Let's start:

From equation 1, we can express 'c' in terms of 'a' and 'b': c = 3 - a - b

Substituting this value of 'c' in equations 2 and 3, we get:

Simplifying these equations further, we have:

Now we can solve these two equations to find the values of 'a' and 'b':

Adding equation 1 and equation 2, we get:

3a - 2b = -10

Multiplying equation 2 by 2, we get:

4a - 2b = -16

Subtracting the second equation from the first equation, we have:

3a - 2b - (4a - 2b) = -10 - (-16)

-a = 6

Therefore, 'a' = -6

Substituting the value of 'a' in equation 1, we get:

-6 - b + 3 - b = 3

-8 - 2b = 0

2b = -8

Therefore, 'b' = -4

Substituting the values of 'a' and 'b' in equation 2, we get:

(-6 + c) - (-4) = 9

-6 + c + 4 = 9

c - 2 = 9

c = 11

So, the three numbers are 'a' = -6, 'b' = -4, and 'c' = 11.

Answer 2

Let the three numbers be x, y, and z.

If the sum of the three numbers is 3, then x+y+z=3

If subtracting the second number from the sum of the first and third numbers gives 9, then x+z-y=9

If subtracting the third number from the sum of the first and second numbers gives -5, then x+y-z=-5

This forms the system of equations:
[1] x+y+z=3
[2] x-y+z=9
[3] x+y-z=-5

First, to find y, let's take do [1]-[2]:
x+y+z=3
-x+y-z=-9
2y=-6
y=-3

Then, to find z, let's do [1]-[3]:
x+y+z=3
-x+-y+z=5
2z=8
z=4

Now that you have y and z, plug them into [1] to find x:
x+y+z=3
x-3+4=3
x=2

So the three numbers are 2,-3, and 4.