SOLUTION: karen is five years younger than susan. three years ago, the sum of their ages was 11. how old are they now? I must show my work and i don't know how ???? please help me !!!!

Question 165665: karen is five years younger than susan. three years ago, the sum of their ages was 11. how old are they now?

I must show my work and i don't know how ???? please help me !!!!!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let k=Karens age (current age) and s=Susan's age (current age)

Since "karen is five years younger than susan", this means that

Now let x=Karen's age 3 years ago and y=Susan's age 3 years ago.

This means that and (simply subtract 3 from both their ages)

Now because "three years ago, the sum of their ages was 11", this tells us that

Plug in and

Plug in

Remove the parenthesis.

Combine like terms on the left side.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce. So Susan is 11 years old (currently)

Go back to the first equation

Plug in

Subtract. So Karen is 6 years old (currently)

==========================================

Answer:

So Karen is currently 6 years old and Susan is 11 years old

Note: To verify this, note that Karen is indeed 5 years younger than Susan. Also, take 3 years off both their ages to get 3 years old for Karen and 8 years old for Susan. Add the ages to get 11. So both of these facts verify our answers.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
karen is five years younger than susan. three years ago, the sum of their ages was 11. how old are they now?
-------------
NOW DATA:
Let Susan be "x" yrs. old ,
Then Karen is "x-5" yrs. old.
---------------------------------
3 years ago DATA:
Susan was "x-3" yrs. old,
Karen was "x-5-3" which is "x-8" yrs. old.
--------------------------------------
EQUATION:
(x-3) + (x-8) = 11
2x - 11 = 11
2x = 22
x = 11 yrs. old (Susan's age now)
x-5 = 11-5 = 6 yrs. old (Karen's age now)
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Cheers,
Stan H.
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