x and y vary inversely. When x=15, then y=6. What will be the value of y when x=9?

Options

A. 10
B. 15
C. 54
D. 135

Answer

To solve the problem step by step, we will use the concept of inverse variation. Here’s how we can find the value of \( y \) when \( x = 9 \):

### Step 1: Understand the relationship
Since \( x \) and \( y \) vary inversely, we can express this relationship as:
\[ x \cdot y = k \]
where \( k \) is a constant.

### Step 2: Find the constant \( k \)
We know that when \( x = 15 \), \( y = 6 \). We can substitute these values into the equation to find \( k \):
\[ 15 \cdot 6 = k \]
Calculating this gives:
\[ k = 90 \]

### Step 3: Set up the equation for the new value of \( x \)
Now that we have the value of \( k \), we can use it to find \( y \) when \( x = 9 \). We set up the equation:
\[ 9 \cdot y = 90 \]

### Step 4: Solve for \( y \)
To find \( y \), we can rearrange the equation:
\[ y = \frac{90}{9} \]
Calculating this gives:
\[ y = 10 \]

### Conclusion
Thus, the value of \( y \) when \( x = 9 \) is:
\[ \boxed{10} \]

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