SOLUTION: The sum of Bob and Carol's age now is 100. Sixteen years ago, Bob was three times as old as Carol. How old was Bob when Carol was born?

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Question 1094638: The sum of Bob and Carol's age now is 100. Sixteen years ago, Bob was three times as old as
Carol. How old was Bob when Carol was born?
Found 3 solutions by josgarithmetic, josmiceli, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
system%28b%2Bc=100%2Cb-16=3%28c-16%29%29

b-16=3c-48
b=3c-48%2B16
b=3c-32
-
3c-32%2Bc=100
4c=132
c=25%2B8
c=33--------Carol now
-
b=67--------Bob now

67-33=highlight%2834%29--------Bob's age when Carol was born

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +b+ = Bob's age now
Let +c+ = Carol's age now
------------------------------
(1) +b+%2B+c+=+100+
(2) +b+-+16+=+3%2A%28+c+-+16+%29+
------------------------------
Add (1) and (2)
(2) +b+-+16+=+3c+-+48+
(2) +-b+%2B+3c+=+32+
(1) +b+%2B+c+=+100+
------------------------
+4c+=+132+
+c+=+33+
and
(1) +b+=+100+-+c+
(1) +b+=+100+-+33+
(1) +b+=+67+
------------------------
The difference in their ages never changes
The difference is: +67+-+33+=+34+ yrs
When Carol was born, +c+-+33+=+0+
and Bob's age was +0+%2B+34+=+34+ yrs old

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Do some logical analysis before you plunge into the algebra, to make the problem easier!

If the sum of their current ages is 100, then 16 years ago that sum was 68.
If 16 years ago Bob was three times as old as Carol, then
x%2B3x+=+68
4x=68
x=17

16 years ago, Carol was x=17 and Bob was 3x=51.
When Carol was born, Bob was 51-17 = 34.