If dogs have 18 more paws than noses, how many dogs are there? - briefly
Dogs are quadrupeds, meaning they have four paws each. Given that dogs also have one nose each, the difference between the number of paws and noses for any number of dogs will always be a multiple of three. Therefore, if there are 18 more paws than noses, there must be exactly 6 dogs.
If dogs have 18 more paws than noses, how many dogs are there? - in detail
To determine the number of dogs given the condition that dogs have 18 more paws than noses, we need to analyze the anatomical characteristics of dogs and set up a mathematical equation.
Dogs are quadrupeds, meaning they have four paws each. Additionally, each dog has one nose. Let's denote the number of dogs as ( d ).
The total number of paws for ( d ) dogs is ( 4d ), since each dog has four paws. The total number of noses for ( d ) dogs is ( d ), since each dog has one nose.
According to the given condition, the number of paws exceeds the number of noses by 18. This can be expressed as:
[ 4d = d + 18 ]
To solve for ( d ), we need to isolate ( d ) on one side of the equation. First, subtract ( d ) from both sides:
[ 4d - d = 18 ]
This simplifies to:
[ 3d = 18 ]
Next, divide both sides by 3:
[ d = \frac{18}{3} ]
[ d = 6 ]
Therefore, there are 6 dogs. This solution is derived from the basic anatomical facts about dogs and the given condition regarding the number of paws and noses. The process involves setting up an equation based on the information provided and solving it step-by-step to find the number of dogs.