If 12 bags of food will feed 6 dogs for 18 days, then how many days will 12 bags of food feed 9 dogs?
The answer is 12 but I just can't see it
Assume that each dog gets the same amount of food.
Thus, each dog will eat 2 bags of food every 18 days (from the given information at the start of the problem).
But that means the dog eats 2/18=1/9 bag per day.
Now, we have to consider feeding the 9 dogs with 12 bags of food. Since each dog eats 1/9 bag per day, that means the 9 dogs eat 1 bag per day. Now, since there are 12 bags available, how many days will it take the 9 dogs to eat them?
If 12 bags of food will feed 6 dogs for 18 days, then how many days will 12 bags of food feed 9 dogs?
12 bags of food will feed 6 dogs for 18 days
Therefore 2 bags of food will feed 1 dog for 18 days
So, $\displaystyle \frac{2}{18}$ bags of food will feed 1 dog for 1 day.
In 1 day, 9 dogs will eat $\displaystyle 9 \times \frac{2}{18}$ bags of food. This means that in 1 day, 9 dogs will eat exactly 1 bag of food.
Therefore with 12 bags of food, it will feed the 9 dogs for 12 days.