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Bunuel
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At a certain restaurant, the ratio of the number of cooks to the numbe 24 Aug 2015, 23:38
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At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

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D
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At a certain restaurant, the ratio of the number of cooks to the numbe 25 Aug 2015, 01:12
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Bunuel
At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

Ans: D

Solution:
c:w = 3:13 ----------------------1
c : w+12 = 3:16 --------------------------2

putting the value of w from 1 to 2
c=12
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At a certain restaurant, the ratio of the number of cooks to the numbe 25 Aug 2015, 04:09
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The ratio of cooks to waiters is 3x:13x, where \(x\) is the unknown multiplier.
\(\frac{3x}{13x+12}=\frac{3}{16}\)
\(9x = 36\)
\(x = 4\)
if \(x(4)\) then \(3*4=12\)

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At a certain restaurant, the ratio of the number of cooks to the numbe 25 Aug 2015, 12:10
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Bunuel
At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

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Cooks:Waiters=3x/13x
Now, 3x/13x+12=3:16
48x=39x+36
9x=36
x=4
3x=12
Answer D
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At a certain restaurant, the ratio of the number of cooks to the numbe 25 Aug 2015, 13:34
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Bunuel
At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

Ans: D

Solution:
c:w = 3:13 ----------------------1
c : w+12 = 3:16 --------------------------2

putting the value of w from 1 to 2
c=12


Hi, I understand the traditional way to answer this and get 12, but I do not understand your method. Would you mind elaborating?
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At a certain restaurant, the ratio of the number of cooks to the numbe 27 Aug 2015, 19:39
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c/w =3/13; c = # of cook and w=# of waiters.
c=3w/13
c/(w+12)=3/16;c=3(w+12)/16.
Therefore, 3(w+12)/16 = 3w/13 => w=156/3=> c=3.w/13=3*156/3*13=12
hence D is the answer
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At a certain restaurant, the ratio of the number of cooks to the numbe 30 Aug 2015, 10:33
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Bunuel
At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

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GROCKIT OFFICIAL SOLUTION:

The key here is setting up the equation. Since we don’t know the initial scale of the number of cooks and waiters, we can express this scale by “x”.

C/W = 3x/13x.

Notice that whatever x is, the ratio will hold true. (x must be an integer, since you can’t have a portion of a cook, unless of course he chops his finger off by accident!)

“When 12 more waiters are hired” is the insertion of an absolute. Adding the 12 waiters, the new ratio becomes:

C/W = 3x/(13x + 12)

“The ratio of the number of cooks to the number of waiters changes to 3 to 16” defines this new ratio:

C/W = 3x/(13x + 12) = 3/16

STOP! Before we cross multiply and solve for x, we want to cancel out the 3’s in both the numerator. (More on this below.) After cross-multiplying, we get:

16x = 13x + 12
3x = 12
x = 4

Sweet. Answer A, right? Well, recall that x represents the scaling factor. The stimulus asks for the number of cooks, which we originally represented by 3x. So, 3*4 = 12 cooks. That’s 120 fingers. Choice D.
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At a certain restaurant, the ratio of the number of cooks to the numbe 26 May 2017, 11:49
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Bunuel
At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

We are given that the ratio of the number of cooks to the number of waiters is 3 to 13 or 3x : 13x.

We are also given that when 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. Thus:

3x/(13x + 12) = 3/16

48x = 3(13x + 12)

48x = 39x + 36

9x = 36

x = 4

Thus, there are 3 x 4 = 12 cooks.

Answer: D
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At a certain restaurant, the ratio of the number of cooks to the numbe 26 Mar 2022, 05:45
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