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Patrick walks by the cookie jar and takes half of the cookies. Then, Debbie walks by and takes 2/5 of what's left. Amy takes 2/3 of what is left after Debbie has been there. If there are now 4 cookies left in the jar, how many were in there to begin with?

 Apr 17, 2021
 #1
avatar+507 
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We can work backwards in this problem:

 

4=1/3 of what is left after Amy has been there, so there were 12 after Debbie took cookies.

 

12=3/5 of what is left after Debbie took the cookies, so there were 20 cookies after Patrick took some.

 

20=1/2 of the original amount of cookies in the jar before Patrick took them, so there were $\boxed{40}$ cookies in the jar to begin with.

 Apr 17, 2021
 #2
avatar+33714 
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Start with 1 whole jar

   remove 1/2     then  1/2 is left

 

    removing  2/5 of the 1/2 leaves 3/5 of the 1/2

          3/5 * 1/2 = 3/10   now are left

 

    removing 2/3 leaves 1/3 of what is left

               1/3  * 3/10 = 3/30 of the original         and this is equal to  4           

                                                3/30 x = 4     x = 4 * 30 /3 = 40 cookies originally

 Apr 17, 2021

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