Question 165665
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+y=11}}}




{{{(k-3)+(s-3)=11}}} Plug in {{{x=k-3}}} and {{{y=s-3}}}




{{{((s-5)-3)+(s-3)=11}}} Plug in {{{k=s-5}}}



{{{s-5-3+s-3=11}}} Remove the parenthesis.



{{{-11+2s=11}}} Combine like terms on the left side.



{{{2s=11+11}}} Add {{{11}}} to both sides.



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



{{{s=(22)/(2)}}} 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.