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Cape Cod Cookies makes cookies of identical size from batches of cooki

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Cape Cod Cookies makes cookies of identical size from batches of cooki  [#permalink]

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New post 04 Apr 2018, 16:20
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Cape Cod Cookies makes cookies of identical size from batches of cookie dough weighing 600 ounces. Cape Cod Cookies decides to modify the recipe by decreasing the weight of each cookie by 1 ounce. If Cape Cod Cookies discovers that it is now able to make 30 more cookies using the same batch of dough weighing 600 ounces, how much did each cookie originally weigh?

A. 2

B. 3

C. 4

D. 5

E. 6

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Re: Cape Cod Cookies makes cookies of identical size from batches of cooki  [#permalink]

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New post 04 Apr 2018, 18:29
1
\(\frac{600}{(x - 1)} - \frac{600}{x} = 30\)

Substitute the options for x, only option D satisfies.

Answer: D
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Re: Cape Cod Cookies makes cookies of identical size from batches of cooki  [#permalink]

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New post 04 Apr 2018, 21:36
1
Let's assume initially there were x cookies each weighing y ounce
As per the question,
x*y=600
(x+30)*(y-1)=600

On solving it we get y=5, which is the required solution.
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Re: Cape Cod Cookies makes cookies of identical size from batches of cooki  [#permalink]

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New post 04 Apr 2018, 22:01
1
carcass wrote:
Cape Cod Cookies makes cookies of identical size from batches of cookie dough weighing 600 ounces. Cape Cod Cookies decides to modify the recipe by decreasing the weight of each cookie by 1 ounce. If Cape Cod Cookies discovers that it is now able to make 30 more cookies using the same batch of dough weighing 600 ounces, how much did each cookie originally weigh?

A. 2

B. 3

C. 4

D. 5

E. 6

Kudos for the right answer and explanation



As shown above too the correct equation is \(\frac{600}{n-1}-\frac{600}{n}=30\)..

EITHER solve it
\(\frac{600}{n-1}-\frac{600}{n}=30...........\frac{20}{n-1}-\frac{20}{n}=1.........20n-20n-20*(-1)=n(n-1)........n(n-1) = 20=5*4.\)..
OR
what you can see is the division by TWO consecutive integers and their difference 30 is multiple of 3..
so either both n and n-1 are MULTIPLE of 3 or both are NOT..
since they are consecutive, both together cannot be multiple of 3, so both will not be multiple of 3..

Only possibility is n and n-1 are 5 and 4..
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Re: Cape Cod Cookies makes cookies of identical size from batches of cooki  [#permalink]

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New post 04 Apr 2018, 22:02
carcass wrote:
Cape Cod Cookies makes cookies of identical size from batches of cookie dough weighing 600 ounces. Cape Cod Cookies decides to modify the recipe by decreasing the weight of each cookie by 1 ounce. If Cape Cod Cookies discovers that it is now able to make 30 more cookies using the same batch of dough weighing 600 ounces, how much did each cookie originally weigh?

A. 2

B. 3

C. 4

D. 5

E. 6

Kudos for the right answer and explanation


Total number of cookies=y
Wt of single cookie =x

Total number of cookies=600/x---1
Total number of cookies +30=600/(x-1)----2

substituting 1 in 2 we get.
600/(x-1)-600/x=30

checking from options

D satisfy..
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Re: Cape Cod Cookies makes cookies of identical size from batches of cooki  [#permalink]

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New post 10 Apr 2018, 11:14
carcass wrote:
Cape Cod Cookies makes cookies of identical size from batches of cookie dough weighing 600 ounces. Cape Cod Cookies decides to modify the recipe by decreasing the weight of each cookie by 1 ounce. If Cape Cod Cookies discovers that it is now able to make 30 more cookies using the same batch of dough weighing 600 ounces, how much did each cookie originally weigh?

A. 2

B. 3

C. 4

D. 5

E. 6


We can let w = original weight of each cookie in ounces and c = the original number of cookies. Thus we have:

wc = 600

When the weight of each cookie is reduced by 1 ounce, the number of cookies is increased by 30, so we have:

(w - 1)(c + 30) = 600

Expanding the second equation we have:

wc + 30w - c - 30 = 600

Since wc = 600, we have:

600 + 30w - c - 30 = 600

30w - c - 30 = 0

Also since wc = 600, c = 600/w. So we have:

30w - 600/w - 30 = 0

Multiply the entire equation by w, we have:

30w^2 - 600 - 30w = 0

w^2 - w - 20 = 0

(w - 5)(w + 4) = 0

w = 5 or w = -4

Since w can’t be negative, w = 5.

Answer: D
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Re: Cape Cod Cookies makes cookies of identical size from batches of cooki   [#permalink] 10 Apr 2018, 11:14
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