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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) (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
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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
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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
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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
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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
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