SOLUTION: Nicole has 3 more dollars than she needs in order to have one-third of the dollars that Kym has. Nicole is 12 dollars short of having half of the dollars that Kym has. How many dol

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Nicole has 3 more dollars than she needs in order to have one-third of the dollars that Kym has. Nicole is 12 dollars short of having half of the dollars that Kym has. How many dol      Log On


   

Question 1201326: Nicole has 3 more dollars than she needs in order to have one-third of the dollars that Kym has. Nicole is 12 dollars short of having half of the dollars that Kym has. How many dollars does Nicole have?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
n, How much Nicole has
k, How much Kym has

system%28n%2B3=%281%2F3%29k%2Cand%2Ck%2F2-n=12%29

Question asks for the value of n.
k-2n=24
k=2n%2B24
-
n%2B3=%281%2F3%29%282n%2B24%29
3n%2B9=2n%2B24
n=24-9
highlight%28n=15%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Nicole has 3 more dollars than she needs in order to have one-third of the dollars that Kym has.
Nicole is 12 dollars short of having half of the dollars that Kym has. How many dollars does Nicole have?
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        In the post by @josgarithmetic,  the setup and the solution
        which follows are incorrect.  I came to bring a correct solution. 


n, How much Nicole has
k, How much Kym has


    n-3 = %281%2F3%29k   (1)

    k%2F2-n = 12     (2)


Multiply 1st equation by 3 (both sides).
Multiply 2nd equation by 2 (both sides).


    3n - 9 =  k      (3)
    k - 2n = 24.     (4)


From (3), substitute expression for k into equation (4)

    (3n-9) - 2n = 24.


Simplify and find n

    3n - 2n = 24 + 9

       n    =    33.


ANSWER.  Nicole has 33 dollars.

Solved.

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For completeness, Kym has 90 dollars.