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. David is five years older tha

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Question 616605: 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 ladyluck4772(11) About Me  (Show Source):
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First, let x=Mike's age because we do not know what it is.

David= x + 5

Sheila is one year older than David so add one to David's age and so forth:

Sheila= x + 6
Nancy = x + 9
Claire = x + 10

Now we know that all of their ages added together equal 120 years. So, we add all of the equations together and put them equal to 120.

(x + 10) + (x + 9) + (x + 6) + (x + 5) + x = 120

Add all like terms

5x + 30 = 120

Subtract 30 from both sides to get the x variable by itself.

5x = 120 - 30
5x = 90

Now divide both sides by 5 to get x by itself.

5x/5 = 90/5
x = 18

x = Mike's age so Mike is 18. Now substitute 18 in the above equations to get each age.

Mike = 18 years old
David = 18 + 5 = 23 years old
Sheila = 18 + 6 = 24 years old
Nancy = 18 + 9 = 27 years old
Claire = 18 + 10 = 28 years old

Now add each age and they will equal 120 years.

18 + 23 + 24 + 27 + 28 = 120
120 = 120