The sum of three numbers is 7. One of the numbers is one more than the sum of the other two numbers. It is also four times the difference between the two numbers.

Question

anonymous · Answer

I got 4, -4, 7 but when you but them back into the equations hey dont work

mathstudent55 · Answer

Let numbers be x, y, and z

The sum of three numbers is 7.
x + y + z = 7

One of the numbers is one more than the sum of the other two numbers.
x = y + z + 1

It is also four times the difference between the two numbers.
x = 4(y - z)

You have 3 equations and 3 unknowns. Now you can solve the system of equations for x, y, and z.

mathstudent55 · Answer

I had an error in the third equation. Now it's correct.

anonymous · Answer

4, 2 , 1

mathstudent55 · Answer

x + y + z = 7   ----->  x +   y   + z = 7
x = y + z + 1    ---->   x -   y   -  z = 1
x = 4(y - z)       ---->   x - 4y + 4z = 0
Now add the first two equations together:
2x = 8
x = 4

mathstudent55 · Answer

4 + y + z = 7
4 - 4y + 4z = 0

y + z = 3
-4y + 4z = -4

4y + 4z = 12
-4y + 4z = -4
8z = 8
z = 1

x + y + z = 7
4 + y + 1 = 7
y = 2

You are correct, 4, 2, 1