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
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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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