If x and y vary inversely and x=18 when y=8, find x when y=16.

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 \( x \) when \( y = 16 \):

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

### Step 2: Find the constant \( k \)
We are given that \( x = 18 \) when \( y = 8 \). We can use these values to find \( k \):
\[ k = x \cdot y = 18 \cdot 8 \]
Calculating this gives:
\[ k = 144 \]

### Step 3: Set up the equation for the new values
Now, we want to find \( x \) when \( y = 16 \). Using the relationship \( x \cdot y = k \), we can write:
\[ x \cdot 16 = 144 \]

### Step 4: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{144}{16} \]
Calculating this gives:
\[ x = 9 \]

### Conclusion
Thus, when \( y = 16 \), the value of \( x \) is \( 9 \).

---