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Etienne began to eat 20 cookies at exactly the same time Jacques began

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Bunuel
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Etienne began to eat 20 cookies at exactly the same time Jacques began [#permalink] New post   09 Jul 2021, 06:45
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Etienne began to eat 20 cookies at exactly the same time Jacques began making more cookies, one at a time, at a constant rate of 16 cookies per hour. If Etienne ate 20 cookies per hour, after how many hours were there no cookies?

A. 3 hours.
B. 4 hours.
C. 5 hours.
D. 6 hours.
E. 7 hours.
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Re: Etienne began to eat 20 cookies at exactly the same time Jacques began [#permalink] New post   09 Jul 2021, 13:41
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There are 20 cookies to start with. Every hour, Etienne eats 20 cookies, and Jacque cooks 16 more. That's a net loss of 4 cookies every hour.

So after one hour, there are 16 cookies, after two hours, 12 cookies, until after five hours, there are no cookies left.

Algebraically:

20 - 20x + 16x = cookies left.

20 - 4x = cookies left.

How long until 0 cookies left?

20 - 4x = 0

So 20 = 4x
So 5 = x.
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Re: Etienne began to eat 20 cookies at exactly the same time Jacques began [#permalink] New post   09 Jul 2021, 13:27
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Bunuel wrote:
Etienne began to eat 20 cookies at exactly the same time Jacques began making more cookies, one at a time, at a constant rate of 16 cookies per hour. If Etienne ate 20 cookies per hour, after how many hours were there no cookies?

A. 3 hours.
B. 4 hours.
C. 5 hours.
D. 6 hours.
E. 7 hours.


The combined rate is \(20 - 16 = 4\) cookies per hour decreased in count. There are 20 cookies in the beginning, so with this rate it will take \(20/4 = 5\) hours to deplete the cookies.

Ans: C
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Re: Etienne began to eat 20 cookies at exactly the same time Jacques began [#permalink] New post   05 Jul 2022, 18:03
ReedArnoldMPREP wrote:
There are 20 cookies to start with. Every hour, Etienne eats 20 cookies, and Jacque cooks 16 more. That's a net loss of 4 cookies every hour.

So after one hour, there are 16 cookies, after two hours, 12 cookies, until after five hours, there are no cookies left.

Algebraically:

20 - 20x + 16x = cookies left.

20 - 4x = cookies left.

How long until 0 cookies left?

20 - 4x = 0

So 20 = 4x
So 5 = x.


ReedArnoldMPREP
I noticed that the answer key from MP says "Note that Etienne eats a lot more than 20 cookies. In 5 hours he eats 100 cookies—the initial 20, plus the 80 that Jacques makes in that 5 hours." I am a bit confused as to why we set the work = 20 cookies then.
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Re: Etienne began to eat 20 cookies at exactly the same time Jacques began [#permalink] New post   06 Jul 2022, 05:04
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woohoo921 wrote:
ReedArnoldMPREP wrote:
There are 20 cookies to start with. Every hour, Etienne eats 20 cookies, and Jacque cooks 16 more. That's a net loss of 4 cookies every hour.

So after one hour, there are 16 cookies, after two hours, 12 cookies, until after five hours, there are no cookies left.

Algebraically:

20 - 20x + 16x = cookies left.

20 - 4x = cookies left.

How long until 0 cookies left?

20 - 4x = 0

So 20 = 4x
So 5 = x.


ReedArnoldMPREP
I noticed that the answer key from MP says "Note that Etienne eats a lot more than 20 cookies. In 5 hours he eats 100 cookies—the initial 20, plus the 80 that Jacques makes in that 5 hours." I am a bit confused as to why we set the work = 20 cookies then.


The '20' in the equation isn't 'work.' The whole equation is not a 'W=RT' equation. It's a 'cookies left' equation. 20 is the original number of cookies. So the equation is:

[Original number of cookies] - [Number of cookies Etienne eats in 'x' hours] + [Number of cookies Jacques bakes in x hours] = [# of cookies remaining]

The number of cookies Etienne eats can be thought of as a 'W=RT' equation: [# cookies eaten = cookies eaten per hour * number of hours = 20x]

The number of cookies Jacques bakes can be 'W=RT' as well: [# cookies baked = cookies baked per hour * number of hours = 16x]

So we end up with:

20 - 20x + 16x = 'cookies remaining'
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Re: Etienne began to eat 20 cookies at exactly the same time Jacques began [#permalink] New post   18 Aug 2023, 03:15
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Re: Etienne began to eat 20 cookies at exactly the same time Jacques began [#permalink]
18 Aug 2023, 03:15
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