The baking time in minutes for a certain cake is defined as `(Vk)/(T)`, where V is the volume of inches cubed, T is the oven temperature in degrees Fahrenheit, and k is a constant. If the baking time was 30 minutes at 350 degrees Fahrenheit for a cake with a volume of 150 cubic inches, what is the value of constant k?

Answer

To find the value of the constant \( k \) in the baking time formula \( \frac{Vk}{T} \), we can follow these steps:

### Step 1: Write down the formula for baking time
The baking time \( t \) is given by the formula:
\[ t = \frac{Vk}{T} \]
where:
- \( V \) is the volume in cubic inches,
- \( T \) is the oven temperature in degrees Fahrenheit,
- \( k \) is the constant we need to find.

### Step 2: Substitute the known values into the formula
We know:
- Baking time \( t = 30 \) minutes,
- Volume \( V = 150 \) cubic inches,
- Temperature \( T = 350 \) degrees Fahrenheit.

Substituting these values into the formula gives:
\[ 30 = \frac{150k}{350} \]

### Step 3: Rearrange the equation to solve for \( k \)
To isolate \( k \), we can multiply both sides by \( 350 \):
\[ 30 \times 350 = 150k \]
This simplifies to:
\[ 10500 = 150k \]

### Step 4: Solve for \( k \)
Now, divide both sides by \( 150 \):
\[ k = \frac{10500}{150} \]

### Step 5: Simplify the fraction
Calculating the right-hand side:
\[ k = 70 \]

### Final Answer
Thus, the value of the constant \( k \) is:
\[ \boxed{70} \]