SOLUTION: Hi After Jenny had given Melissa 16 stickers both had the same number of stickers. Linda then gave 24 stickers to Jenny and the ratio of the number of stickers Jenny had to the or

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Question 1185481: Hi
After Jenny had given Melissa 16 stickers both had the same number of stickers. Linda then gave 24 stickers to Jenny and the ratio of the number of stickers Jenny had to the original number of Melissa's stickers became 5 to 1.
How many did Jenny have at first.
Thanks
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
 STEPS         Jenny          Melissa         Linda
 original      j              m               L
  1            j-16           m+16            L
  2            j-16+24        m+16            L-24

Some details of description
allow this system of equations:
system%28%28j-16%2B24%29%2Fm=5%2Cj-16=m%2B16%29

system%28j%2B8=5m%2Cj-m=32%29

system%28-j%2B5m=8%2Cj-m=32%29
Add corresponding members.

4m=40
highlight%28m=10%29

j-m=32
j=32%2Bm
j=32%2B10
highlight%28j=42%29

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
After Jenny had given Melissa 16 stickers both had the same number of stickers.
Linda then gave 24 stickers to Jenny and the ratio of the number of stickers Jenny had
to the original number of Melissa's stickers became 5 to 1.
How many did Jenny have at first ?
~~~~~~~~~~~~~~~~ 

Let J be the number of stickers Jenny had at first; 

    M be the number of stickers Melissa had at first.


After Jenny had given Melissa 16 stickers, we have


    J - 16 = M + 16,   or   M = J - 32.


Linda then gave 24 stickers to Jenny.  Now Jenny has


    J - 16 + 24 = J + 8.


Next, problem states that


    %28J+%2B+8%29%2FM = 5%2F1,   or   %28J%2B8%29%2F%28J-32%29 = 5.


To solve this equation, multiply both sides by (J-32) and simplify then.   You will get


    J + 8 = 5*(J-32)

    J + 8 = 5J - 160

    160 + 8 = 5J - J

       168  = 4J

         J  =  168/4 = 42.


ANSWER.  At first, Jenny had 42 stickers.

Solved.