If y varies inversely as x and x = 3 when y =4. Find the value of x when y = 12

1. Analyze the question

We are given that $y$ varies inversely as $x$. We are provided with an initial pair of values ($x=3, y=4$) and asked to find the new value of $x$ when $y=12$.

2. Explain the concept

In mathematics, when $y$ varies inversely as $x$, it means that their product is always a constant ($k$). The relationship is expressed as:

This can also be written as:

Where $k$ is the constant of variation.

3. Show the solution

Step 1: Find the constant ($k$) using the initial values. Given $x = 3$ and $y = 4$:

Step 2: Use the constant to find the new value of $x$. Now we know the relationship is $xy = 12$. We need to find $x$ when $y = 12$:

Divide both sides by 12:

4. Identify the answer

Comparing our result to the given options: A. 4 B. 1 C. 2 D. 3

The correct option is B.

5. Tip

For inverse variation problems, always remember the "Product Rule": $x_1y_1 = x_2y_2$. This allows you to skip finding the constant $k$ entirely and solve the equation directly: $3 \times 4 = x_2 \times 12$ $12 = 12x_2$ $x_2 = 1$