The cost of production of a certain instrument is directly proportional to the number of units produced. The cost of production for 300 units is $300. What is the cost of production for 270 units?

Options

A. 270
B. 300
C. 325
D. 370

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the relationship between cost and units produced
The problem states that the cost of production (C) is directly proportional to the number of units produced (N). This can be expressed mathematically as:
\[ C = kN \]
where \( k \) is the constant of proportionality.

**Hint:** Remember that "directly proportional" means that as one quantity increases, the other increases at a constant rate.

### Step 2: Find the constant of proportionality (k)
We know that for 300 units produced, the cost is $300. We can substitute these values into the equation to find \( k \):
\[ 300 = k \times 300 \]

To find \( k \), we can rearrange the equation:
\[ k = \frac{300}{300} = 1 \]

**Hint:** When you have a direct proportionality, you can find the constant by dividing the cost by the number of units.

### Step 3: Write the equation with the constant
Now that we have found \( k \), we can write the equation for cost as:
\[ C = 1 \times N \]
or simply:
\[ C = N \]

**Hint:** The equation simplifies to \( C = N \) when \( k = 1 \).

### Step 4: Calculate the cost for 270 units
Now we need to find the cost of production for 270 units. We can substitute \( N = 270 \) into the equation:
\[ C = 270 \]

**Hint:** Substitute the number of units directly into the simplified equation to find the cost.

### Conclusion
The cost of production for 270 units is $270.

**Final Answer:** $270