SOLUTION: Claire is one year older than her sister Nancy. Nancy is three years ___________ ___________ __ older than her sister Sheila. Sheila is one year older than her brother David.

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Question 715157: Claire is one year older than her sister Nancy. Nancy is three years __________________________
older than her sister Sheila. Sheila is one year older than her brother
David. David is five years older than his brother Mike. The sum of
the five siblings’ ages is 120 years. Find the age of each.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Claire is one year older than her sister Nancy.
C = N + 1

Nancy is three years older than her sister Sheila.
N = S + 3

Sheila is one year older than her brother David.
S = D + 1  

David is five years older than his brother Mike.
D = M + 5

The sum of the five siblings’ ages is 120 years.
C + N + S + D + M = 120

So we have the five equations in five unknowns:


C = N + 1
N = S + 3
S = D + 1
D = M + 5
C + N + S + D + M = 120

Align the like letters into columns:

C - N             =   1
    N - S         =   3
        S - D     =   1
            D - M =   5
C + N + S + D + M = 120

Add the last two equations and the M's cancel:

             D - M =   5
C + N + S +  D + M = 120
------------------------
C + N + S + 2D     = 125

So now we have 4 equations in 4 unknowns:

C - N           =   1
    N - S       =   3
        S -  D  =   1
C + N + S + 2D  = 125

Multiply the 3rd equation by 2 and add to the fourth
equations and the D's will cancel:


        2S - 2D  =   2
C + N +  S + 2D  = 125
----------------------
C + N + 3S       = 127

So now we have 3 equations and 3 unknowns:

C - N      =   1
    N - S  =   3
C + N + 3S = 127

Multiply the 2nd equation by 3 and add to the second
equation and the S's will cancel:

    3N - 3S =   9
C +  N + 3S = 127
-----------------
C + 4N      = 136

So now we have 2 equations and 2 unknowns:

C -  N =   1
C + 4N = 136

Multiply the 1st equation by -1 and add to the second
equation and the C's will cancel:

-C +  N =  -1
 C + 4N = 136
-------------
     5N = 135
      N = 27

Sunstitute 27 for N in 

 C - N = 1
C - 27 = 1
     C = 28

and in

 N - S = 3
27 - S = 3
    -S = -24
     S = 24

Substitute 24 for S in

 S - D = 1
24 - D = 1
    -D = -23
     D = 23 

Substitute 23 for D in:

     D - M = 5
    23 - M = 5
        -M = -18
         M = 18

Claire is 28, Nancy is 27, Sheila is 24, David is 23, Mike is 18.

Checking:

Claire 28, is one year older than her sister Nancy, 27.  Nancy, 27, is 
three years older than her sister Sheila, 24.  Sheila, 24, is one year 
older than her brother David, 23.  David is five years older than his 
brother Mike, 18.  The sum of the five siblings’ ages is 
28+27+24+23+18 = 120 years. 

Edwin