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# Fraction

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42
2

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
+496
0

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
+31648
+1

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