If there are 18 more paws than noses, how many dogs are there? - briefly
If there are 18 more paws than noses, it implies that there are 9 dogs. This is because each dog has 4 paws and 1 nose, so the difference of 18 paws accounts for 9 additional dogs.
If there are 18 more paws than noses, how many dogs are there? - in detail
To determine the number of dogs based on the given information that there are 18 more paws than noses, we need to delve into the anatomy and basic mathematics involved in this problem.
Dogs, like most mammals, have four legs, which translates to four paws. Therefore, each dog contributes four paws to the total count. On the other hand, dogs have only one nose each. This fundamental biological fact allows us to set up a mathematical relationship between the number of noses and paws.
Let ( D ) represent the number of dogs. Since each dog has one nose, the total number of noses is also ( D ). Similarly, since each dog has four paws, the total number of paws is ( 4D ).
According to the problem, there are 18 more paws than noses. This can be expressed as: [ 4D = D + 18 ]
To solve for ( D ), we need to isolate it on one side of the equation. Subtracting ( D ) from both sides gives us: [ 3D = 18 ]
Dividing both sides by 3 yields: [ D = 6 ]
Therefore, there are 6 dogs. This result is consistent with our understanding of canine anatomy and basic arithmetic principles. By breaking down the problem into its core components—the number of paws and noses per dog—and applying simple algebraic manipulation, we arrive at a clear and definitive answer.