Mr. Joshi has 430 cabbage - plants which he wants to plant out, some 25 to a row, the rest 20 to a row. If there are to be 18 rows in all, how many rows of 25 will there be ? 

Options

A. 10
B. 14
C. 8
D. 12

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Variables
Let \( x \) be the number of rows with 25 cabbage plants.

### Step 2: Determine the Number of Rows with 20 Plants
Since there are a total of 18 rows, the number of rows with 20 plants will be \( 18 - x \).

### Step 3: Set Up the Equation for Total Plants
The total number of cabbage plants can be expressed as:
\[ 25x + 20(18 - x) = 430 \]
Here, \( 25x \) represents the total number of plants in the rows with 25 plants, and \( 20(18 - x) \) represents the total number of plants in the rows with 20 plants.

### Step 4: Simplify the Equation
Now, let's simplify the equation:
\[ 25x + 20(18) - 20x = 430 \]
Calculating \( 20 \times 18 \):
\[ 25x + 360 - 20x = 430 \]

### Step 5: Combine Like Terms
Combine the terms involving \( x \):
\[ (25x - 20x) + 360 = 430 \]
This simplifies to:
\[ 5x + 360 = 430 \]

### Step 6: Isolate \( x \)
Subtract 360 from both sides:
\[ 5x = 430 - 360 \]
Calculating the right side gives:
\[ 5x = 70 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 5:
\[ x = \frac{70}{5} = 14 \]

### Conclusion
Thus, the number of rows with 25 cabbage plants is \( 14 \).