# There are people walking their dogs at a park. There are 30 heads and 68 feet at the park. Write...

## Question:

There are people walking their dogs at a park. There are 30 heads and 68 feet at the park. Write out the algebraic equations for this problem. Use P to stand for the number of people and D to stand for the number of dogs.

## Algebraic Expressions:

Algebraic expressions are used to mathematically describe sentences. They are used in various subjects such as Chemistry, Biology, and Physics to describe laws and properties of real life instances.

As given in the problem, let {eq}P {/eq} stand for the number of people and {eq}D {/eq} stand for the number of dogs. Since there are 30 total heads and both dogs and humans only have one head (we will assume) then

{eq}30 = P+D {/eq}

Now, each dog we will assume has 4 feet giving a total of {eq}4D {/eq} feet from the dogs. Each person we will assume has 2 feet giving a total of {eq}2P {/eq} feet from the people. Since there are a total of 68 feet, we get the expression

{eq}68 = 4D + 2P {/eq}

These together give the following system of equations

{eq}\begin{cases} 30 = D + P\\ 68 = 4D + 2P \end{cases} {/eq} 