In a family with five heads and fourteen legs, how many are people, and how many are dogs? - briefly
To determine the composition of a household consisting of five heads and fourteen legs, we need to consider the typical anatomical features of humans and dogs. Humans have one head and two legs, while dogs have one head and four legs.
There are four people and one dog.
In a family with five heads and fourteen legs, how many are people, and how many are dogs? - in detail
To determine the number of people and dogs in a scenario where there are five heads and fourteen legs, we need to consider the biological characteristics of humans and dogs. Humans typically have one head and two legs, while dogs have one head and four legs. Let's break down the problem step-by-step.
First, we need to establish the equations based on the given information. Let ( P ) represent the number of people and ( D ) represent the number of dogs. We can set up the following system of equations:
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The total number of heads is five: [ P + D = 5 ]
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The total number of legs is fourteen: [ 2P + 4D = 14 ]
Next, we solve these equations to find the values of ( P ) and ( D ). We start by solving the first equation for ( P ): [ P = 5 - D ]
Now, substitute ( P ) in the second equation: [ 2(5 - D) + 4D = 14 ] [ 10 - 2D + 4D = 14 ] [ 2D = 4 ] [ D = 2 ]
Now that we have the value of ( D ), we substitute it back into the equation for ( P ): [ P = 5 - 2 ] [ P = 3 ]
Therefore, in this scenario, there are 3 people and 2 dogs. This solution is derived from the biological facts that humans have one head and two legs, while dogs have one head and four legs, and the given total counts of heads and legs.