If `xy=k`, where k is a constant and `y=21`, when `x=6`, what is the value of y when `x=9`?

Answer

To solve the problem step by step, let's follow the given information and apply the necessary calculations.

### Step 1: Understand the relationship between x, y, and k
We are given the equation:
\[ xy = k \]
where \( k \) is a constant.

### Step 2: Substitute the known values to find k
We know that \( y = 21 \) when \( x = 6 \). We can substitute these values into the equation to find \( k \):
\[ k = xy \]
Substituting the values:
\[ k = 6 \times 21 \]
\[ k = 126 \]

### Step 3: Use the value of k to find y when x = 9
Now we need to find the value of \( y \) when \( x = 9 \). We will use the same equation:
\[ xy = k \]
Substituting the known values:
\[ 9y = 126 \]

### Step 4: Solve for y
To find \( y \), we can rearrange the equation:
\[ y = \frac{k}{x} \]
Substituting the values we have:
\[ y = \frac{126}{9} \]
Calculating this gives:
\[ y = 14 \]

### Final Answer
The value of \( y \) when \( x = 9 \) is \( 14 \).

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