Question 134417
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+5}}}


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+5}}} to get {{{(1/2)(f+5)}}}



Now set the two expressions {{{f-13}}} and {{{(1/2)(f+5)}}} equal to each other


{{{f-13=(1/2)(f+5)}}}





{{{(2)(f-13)=cross(2)((1/cross(2))(f+5))}}} Multiply both sides by  2.



{{{2f-26=f+5}}} Multiply




{{{2f=f+5+26}}}Add 26 to both sides



{{{2f-f=5+26}}} Subtract f from both sides



{{{f=5+26}}} 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+5=36}}}


And we can see that 18 is half of 36



So we can see that our answer is correct.