Questions: If A is cut in half while B and C are held constant, the new value of X will be times the original value.
Transcript text: If $A$ is cut in half while $B$ and $C$ are held constant, the new value of $X$ will be $\qquad$ times the original value.
Solution
Solution Steps
To solve this problem, we need to understand the relationship between variables \( A \), \( B \), \( C \), and \( X \). Assuming \( X \) is a function of \( A \), \( B \), and \( C \), we need to determine how halving \( A \) affects \( X \). Without a specific function provided, we can only outline a general approach. If \( X \) is directly proportional to \( A \), then halving \( A \) would halve \( X \). If \( X \) is inversely proportional to \( A \), then halving \( A \) would double \( X \). The exact relationship needs to be defined to provide a precise answer.
Step 1: Understand the Relationship
Assume that the variable \( X \) is directly proportional to \( A \), meaning \( X = k \cdot A \), where \( k \) is a constant that depends on \( B \) and \( C \).
Step 2: Modify the Variable \( A \)
Given that \( A \) is cut in half, the new value of \( A \) becomes \( \frac{A}{2} \).
Step 3: Calculate the New Value of \( X \)
Substitute the new value of \( A \) into the proportional relationship:
\[
X_{\text{new}} = k \cdot \frac{A}{2} = \frac{k \cdot A}{2} = \frac{X_{\text{original}}}{2}
\]
Step 4: Determine the Factor of Change
The new value of \( X \) is \( \frac{1}{2} \) times the original value of \( X \).
Final Answer
The new value of \( X \) is \(\boxed{0.5}\) times the original value.