SOLUTION: Adam is three times as old as Cynthia and Fred is sixteen years younger than Adam. One year ago, Adams age was twice the sum of Cynthia's and Fred's age. Find their present age.

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Question 185095: Adam is three times as old as Cynthia and Fred is sixteen years younger than Adam. One year ago, Adams age was twice the sum of Cynthia's and Fred's age. Find their present age.
Answer by ZeratuelX(5) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+Adam%27s+Age
C+=+Cynthia%27s+Age
F+=+Fred%27s+Age
A+=+3C
F+=+A-16
A-1+=+2%28C%2BF%29
If we simplify the lines to solve for A we get:
A+=+3C
A+=+F%2B16
A+=+2C%2B2F%2B1
Since the lines are all equal to A, we can set them equal to each other (if a=b, and b=c, then a=c).
3C+=+F%2B16
3C+=+2F%2B2C%2B1
After some more simplifying we get this:
3C+=+F++%2B16
C++=+2F+%2B1
Multiply the top equation by 2 so that we can use elimination to remove F.
6C+=+2F+%2B32
C++=+2F+%2B1
Subtract them out (elimination)
6C-C+=+2F-2F%2B32-1
5C+=+31
C+=+31%2F5
C+=+6.2
We have found Cynthia's Age, which is 6.2 years. Now let's plug this back in to the original equations:
A+=+3C
A+=+3%286.2%29
A+=+18.6
Adam is 18.6 years old. Let's plug into the final equation to find Fred's age.
A+=+F%2B16
%2818.6%29-16+=+F
F+=+2.6
Fred is 2.6 years old. Now lets plug back in and check our work.
A+=+3C
%2818.6%29+=+3%286.2%29++check.
A+=+F%2B16
%2818.6%29+=+%282.6%29%2B16++check.
A+=+2C%2B2F%2B1
%2818.6%29+=+2%286.2%29%2B2%282.6%29%2B1
18.6+=+12.4%2B5.2%2B1++check.
So we have found all the correct ages.
Answers:
Adam+=+18.6+years
Cynthia+=+6.2+years
Fred+=+2.6+years