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 $.