SOLUTION: My problem : At a recent birthday party for a friend of mine, I pointed out the following to my friend: Thirteen years ago, you were half as old as you will be five years from no

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Question 134417: My problem : At a recent birthday party for a friend of mine, I pointed out the following to my friend: Thirteen years ago, you were half as old as you will be five years from now. What was my friend's age?

I have no work to show on this one because the sample(below) shows that Im doing formula all wrong....Please help me see where I am going wrong. Its been a while and Im obviously close but too rusty :P
SAMPLE: At a recent birthday party for a friend of mine, I pointed out the following to my friend: Eighty-eight years ago, you were one-third as old as you will be six years from now.
My answer: 123 correct answer was 135
Sample problem solutions 88+6=94/3=31+94=125 or 88/3=29+88+6=123
Thank you really for taking the time having done tutoring myself I appreciate what you guys are doing here.
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be your friend's age.
Given : %28x-13%29+=+%28x%2B5%29%2F2
2%28x-13%29+=+x%2B5
2x+-+26+=+x+%2B+5+
x+=+31
Check your answer. Is 31 - 13 equal to (31+5)/2 ???

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let f=age of friend


The phrase "13 years ago" can be written as f-13 and the phrase "five years from now" can be written as f%2B5

Now since "Thirteen years ago, you were half as old as you will be five years from now", this means that we simply take half of f%2B5 to get %281%2F2%29%28f%2B5%29


Now set the two expressions f-13 and %281%2F2%29%28f%2B5%29 equal to each other

f-13=%281%2F2%29%28f%2B5%29




%282%29%28f-13%29=cross%282%29%28%281%2Fcross%282%29%29%28f%2B5%29%29 Multiply both sides by 2.


2f-26=f%2B5 Multiply



2f=f%2B5%2B26Add 26 to both sides


2f-f=5%2B26 Subtract f from both sides


f=5%2B26 Combine like terms on the left side


f=31 Combine like terms on the right side

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Answer:
So our answer is f=31

This means that the friend is 31 years old

Notice how if we subtract 13 from 31 we get 31-13=18. So 13 years ago s/he was 18


Now add 5 to 31 to get 31%2B5=36

And we can see that 18 is half of 36


So we can see that our answer is correct.