At a certain restaurant, the ratio of the number of cooks to the numbe

Question

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

Kudos for a correct solution.

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

Kudos for a correct  solution .

D3N0 · Answer

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

mejia401 · Answer

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

Kr,
Mejia

KS15 · Answer

Cooks:Waiters=3x/13x
Now, 3x/13x+12=3:16
48x=39x+36
9x=36
x=4
3x=12
Answer D

dimplesandanmba · Answer

Hi, I understand the traditional way to answer this and get 12, but I do not understand your method. Would you mind elaborating?

lipsi18 · Answer

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

Bunuel · Answer

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.

JeffTargetTestPrep · Answer

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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