The first o9f three

Question

The first of three numbers exceeds the third by one half of he second. The sum of the second and third numbers is one more than the first. If the second is subtracted from the sum of the first and third numbers the result is 5. Determine the numbers

Answer 1

Call the numbers x, y, z

 

x = z + y/2  _______ eqn 1

 

y + z = x + 1 ______ eqn 2

 

x + z - y = 5 ______ eqn 3

 

Lets rearrange equations to put all

variables on the left.

 

x - y/2 - z = 0 _____ eqn 1

-x + y + z = 1 _____ eqn 2

x - y + z = 5 ______ eqn 3

 

Let's add equation 1 and equation 2

 

x - y/2 - z = 0

-x + y + z = 1

------------------

    (1/2)y = 1

      y = 2

 

Let's add equations 1 and 3

 

x - y/2 - z = 0

x - y + z = 5

-------------------

2x - (3/2)y = 5

2x - (3/2)(2) = 5

2x - 3 = 5

2x = 8

x = 4

 

Substitute the values of x and y into one of the

original equations to solve for z.  Let's

use equation 3.

 

x - y + z = 5

4 - 2 + z = 5

2 + z = 5

z = 3

 

Your numbers are {4, 2, 3}

 

You can check by plugging these values into the

original equations as x, y, z respectively to verify

the equations balance.