- Define the number of dogs as \(x\).
- Translate the relationship into the equation: \(4x = 16\).
- Solve by dividing both sides by 4: \(x = 4\).
- The correct choice is: \(\boxed{4x = 16; x = 4}\).
Explanation
- Problem Analysis and Variable Assignment
The problem asks us to determine the number of dogs Julie has, given that she has 16 chickens and the number of chickens is four times the number of dogs. Let \(x\) represent the number of dogs. Since the number of chickens is 16 and this is four times the number of dogs, we can express this relationship mathematically as the number of chickens being equal to 4 times the number of dogs.
- Formulating the Equation
We set up the equation based on the given relationship. We know that the total number of chickens is 16 and that there are four times as many chickens as dogs. Therefore, we can write the equation:
\[4x = 16\]
where \(x\) represents the number of dogs.
- Solving the Equation
To solve for \(x\), we need to isolate the variable on one side of the equation. We divide both sides of the equation by 4:
\[x = \frac{16}{4}\]
\[x = 4\]
Thus, Julie has 4 dogs. This matches the first given option, \(4x = 16; x = 4\).
Examples
This type of algebraic reasoning is useful in everyday scenarios involving ratios and quantities. For instance, if you are baking cookies and know that each batch requires 4 cups of flour, and you have 16 cups of flour available, you can use the equation \(4x = 16\) to determine that you can make \(x = 4\) batches. This helps in efficient resource management and planning.