Question 224466
Let k = Kim's present age
Let s = Sue's present age
:
Write an equation for each statement:
:
"kim is 1/3 the age of her older sister sue."
k = {{{1/3}}}s
or
s = 3k; may use it this way for substitution
;
" in 13 years, sue will be one year younger than twice kim's age."
s + 13 = 2(k + 13) - 1
Simplify the equation as much as possible 
s + 13 = 2k + 26 - 1
s + 13 = 2k + 25
s = 2k + 25 - 13
s = 2k + 12
:
 how old is sue?
:
Substitute 3k for s in the above equation, find k
3k = 2k + 12
3k - 2k = 12
k = 12 yrs is Kim's present age
then
s = 3k
s = 3(12)
s = 36 is Sue's present age
;
:
Check our solution in the statement:
"in 13 years, sue will be one year younger than twice kim's age.
36 + 13 = 2(12 + 13) - 1
49 = 2(25) - 1; confirms our solution 
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Did this make sense to you?