The sum of three numbers is 65

Question

The sum of three numbers is 65. The third number minus the first number is 15 less than the second number.Twice the first number is 23. Find the three numbers 

Answer 1

A + B + C = 65

 

C - A = B - 15

 

2A = 23

 

Now that we have written those correctly, we can first solve A pretty easily.  2A = 23, so A = 11.5.

 

The first equation can now be written as B + C = 53.5

The second equation can now be written as C - 11.5 = B - 15 ... Transform to 3.5 = B - C

 

You can add those two equations together:

 

B - C = 3.5

B + C = 53.5

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

2B = 57

B = 28.5

 

Now find C using one of the previous equations and substituting B.  28.5 + C = 53.5 ... C = 25.

 

Check your work.  A + B + C = 65 ... 11.5 + 28.5 + 25 = 65, check.

C - A = B - 15

25 - 11.5 = 28.5 - 15 ... 13.5 = 13.5, check.

Answer 2

Let the 3 numbers be a, b and c

Given: a+b+c=65   ----> equation 1

          c-a=b-15

          subtracting b from both sides,

         c-a-b = b-15-b

or -a-b+c=-15  ---> equation 2

 

2a = 23  or a = 23/2

                 a=11.5

Adding equations 1 and 2,

 a+b+c=65

-a-b+c=-15

     c+c=65-15=50

    or, 2c=50

    or, c=50/2  c=25

Substitute the values of a and c in equation 1,

11.5+b+25=65

11.5+b=65-25=40

or b = 40-11.5 or b=28.5