SOLUTION: It takes 3 cats 3 minutes to catch 3 mice. How many cats are needed to catch 99 mice in 99 minutes? A)3 B)11 C)33 D)99

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Question 1143029: It takes 3 cats 3 minutes to catch 3 mice. How many cats are needed to catch 99 mice in 99 minutes?
A)3
B)11
C)33
D)99

Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


There are many different ways to look at problems like this. Here are a couple of ways that work for me. Possibly you will get responses from other tutors showing other methods; you might like one of them better....

(1) The 3 cats together catch 3 mice in 3 minutes, so their rate of catching mice is 1 per minute. So the same 3 cats will catch 99 mice in 99 minutes.

(2) Changing the number of mice from 3 to 99 multiplies the required number of cats by 99/3 = 33. Then changing the number of minutes from 3 to 99 DIVIDES the required number of cats by 99/3 = 33. So you end up requiring the same number of cats.

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

            Surely,  if you strength your logical skills,  you can solve the problem as the tutor @greenestamps suggests.

            But there is an Algebra way,  where you don't need to strength - you need to follow the standard procedure,  only.


The rate of work of each cat in catching mice is   3 mice divided by 3 cats and 3 minutes, which is 


     =  of the mouse per cat per minute.


For another scenarious, the rate of work per cat per minute is the same


     = ,

or

     = .         (1)


where  x  is the unknown number of cats.


From the proportion (1), you have, of course,  x = 3    cats.    ANSWER

-------------

To see many other similar solved problems, look into the lesson
    - Rate of work problems
in this site.

It is good to have both these methods at your possession.



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