If `y=kx`, where k is a constant and `y=27` when `x=18`, what is the value of y when `x=30`?

Answer

To solve the problem step by step, we will follow the given equation \( y = kx \) and the provided values.

### Step 1: Identify the given values
We know that:
- \( y = 27 \) when \( x = 18 \)

### Step 2: Substitute the values into the equation to find \( k \)
Using the equation \( y = kx \):
\[ 27 = k \cdot 18 \]
To find \( k \), we can rearrange this equation:
\[ k = \frac{27}{18} \]

### Step 3: Simplify the value of \( k \)
Now, simplify \( \frac{27}{18} \):
\[ k = \frac{27 \div 9}{18 \div 9} = \frac{3}{2} \]

### Step 4: Use the value of \( k \) to find \( y \) when \( x = 30 \)
Now that we have \( k = \frac{3}{2} \), we can find \( y \) when \( x = 30 \):
\[ y = kx = \frac{3}{2} \cdot 30 \]

### Step 5: Calculate \( y \)
Now, calculate \( y \):
\[ y = \frac{3 \cdot 30}{2} = \frac{90}{2} = 45 \]

### Final Answer
Thus, the value of \( y \) when \( x = 30 \) is \( \boxed{45} \).

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