9514 1404 393
Answer:
- Sarah is 7
- Bob is 14
- Nellie is 17
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
__
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.
