- Define the number of dogs as \(x\).
- Translate the problem into the equation \(4x = 16\).
- Divide both sides by 4 to solve for \(x\), which gives \(x = 4\).
- The correct option is \(\boxed{4x = 16; x = 4}\).
Explanation
- Problem Analysis and Variable Definition
We are given that Julie has a total of 16 chickens. We are also told that she has 4 times as many chickens as she has dogs. Let \(x\) represent the number of dogs Julie has. Based on the information provided, we can express the number of chickens in terms of the number of dogs as \(4 \times x\). Since we know the total number of chickens is 16, we can set up the equation \(4x = 16\).
- Solving the Equation
To find the number of dogs, we solve the equation \(4x = 16\). Dividing both sides of the equation by 4 gives:
\[x = \frac{16}{4} = 4\]
Thus, Julie has 4 dogs. Comparing this to the given options, the equation \(4x = 16\) leads to \(x = 4\).
Examples
In everyday life, understanding relationships between different quantities is crucial. For instance, if a bakery makes 4 times as many chocolate chip cookies as sugar cookies, and you know they made 16 chocolate chip cookies, you can easily calculate that they made 4 sugar cookies. This type of basic algebraic reasoning helps in resource management, cooking, and shopping, ensuring you always know how much of each item you have!