Sarah, Bob and Nellie are cousins. Sarah is half the age of Bob. In three years time Nellie will be twice as old as Sarah. Their ages at the moment add to 38 years. Determine the ages of Sarah, Bob and Nellie

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Step-by-step explanation:

Let s, b, n represent the current ages of Sarah, Bob, and Nellie, respectively.

  s = b/2 . . . . . . Sarah is half Bob's age

  2(s+3) = n+3 . . . . in 3 years, Nellie will be twice Sarah's age

  s + b + n = 38 . . . . . their ages now add to 38

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We can rearrange the first two equations to find Bob and Nellie's age in terms of Sarah's. Then we can substitute into the third equation to find Sarah's age.

  b = 2s . . . . . . multiply the first equation by 2

  2s +3 = n . . . . subtract 3 from the second equation and simplify

  s +(2s) +(2s+3) = 38 . . . . substitute for b and n

  5s = 35 . . . . . . . . . . . . subtract 3, collect terms

  s = 7 . . . . . . . . . . . . divide by 5

  b = 2(7) = 14

  n = 2(7) +3 = 17

Sarah is 7, Bob is 14, and Nellie is 17.