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Mr. Venado makes a batch of cookies for his math class. Aaron takes 1/6the of the cookies and runs out the door. Matthew then takes 1/5th of the cookies that are left. Paige takes 1/4th of what remains after Matthew leaves. Jodh takes 1/3rd of what remains after Paige, and then Dylan grabs half of the remaining cookies after Jodh. Gavin then swoops in and grabs the last remaining 6 cookies. How many cookies were in the batch to begin with?

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Answer:

To determine the number of cookies in the batch at the beginning, let's break down the problem step by step.

1. Aaron takes 1/6th of the cookies, leaving 5/6th of the original batch.

2. Matthew then takes 1/5th of the remaining cookies, leaving 4/5th of the 5/6th.

3. Paige takes 1/4th of what remains after Matthew, leaving 3/4th of the 4/5th.

4. Jodh takes 1/3rd of what remains after Paige, leaving 2/3rd of the 3/4th.

5. Dylan grabs half of the remaining cookies after Jodh, leaving 1/2 of the 2/3rd.

6. Finally, Gavin swoops in and grabs the last remaining 6 cookies.

Now, let's calculate the number of cookies left at each step:

1. 5/6th of the original batch after Aaron = (5/6) * original batch

2. 4/5th of the 5/6th after Matthew = (4/5) * (5/6) * original batch

3. 3/4th of the 4/5th after Paige = (3/4) * (4/5) * (5/6) * original batch

4. 2/3rd of the 3/4th after Jodh = (2/3) * (3/4) * (4/5) * (5/6) * original batch

5. 1/2 of the 2/3rd after Dylan = (1/2) * (2/3) * (3/4) * (4/5) * (5/6) * original batch

Since Gavin takes the last remaining 6 cookies, we can set the equation:

(1/2) * (2/3) * (3/4) * (4/5) * (5/6) * original batch = 6

Now, we can solve for the original batch:

(1/2) * (2/3) * (3/4) * (4/5) * (5/6) * original batch = 6

Simplifying the equation, we have:

(1/6) * original batch = 6

Multiplying both sides by 6, we find:

original batch = 36

Therefore, the batch initially had 36 cookies.

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