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 !!!!

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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) About Me  (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 k=s-5


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

This means that x=k-3 and y=s-3 (simply subtract 3 from both their ages)


Now because "three years ago, the sum of their ages was 11", this tells us that x%2By=11



%28k-3%29%2B%28s-3%29=11 Plug in x=k-3 and y=s-3



%28%28s-5%29-3%29%2B%28s-3%29=11 Plug in k=s-5


s-5-3%2Bs-3=11 Remove the parenthesis.


-11%2B2s=11 Combine like terms on the left side.


2s=11%2B11 Add 11 to both sides.


2s=22 Combine like terms on the right side.


s=%2822%29%2F%282%29 Divide both sides by 2 to isolate s.


s=11 Reduce. So Susan is 11 years old (currently)


k=s-5 Go back to the first equation


k=11-5 Plug in s=11


k=6 Subtract. So Karen is 6 years old (currently)


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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) About Me  (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?
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NOW DATA:
Let Susan be "x" yrs. old ,
Then Karen is "x-5" yrs. old.
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3 years ago DATA:
Susan was "x-3" yrs. old,
Karen was "x-5-3" which is "x-8" yrs. old.
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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.