8 pens and 3 pencils cost as much as 3 pens and 9 pencils. What is the ratio of the cost of one pen to the cost of one pencil?

Options

A. A)`5:4`
B. B)`6:7`
C. C)`6:5`
D. D)`3:2`

Answer

To solve the problem, we need to set up an equation based on the information given. Let's denote the cost of one pen as \( P \) and the cost of one pencil as \( p \).

### Step-by-Step Solution:

1. **Set up the equation based on the problem statement:**
According to the problem, the cost of 8 pens and 3 pencils is equal to the cost of 3 pens and 9 pencils. We can express this mathematically as:
\[ 8P + 3p = 3P + 9p \]

2. **Rearrange the equation:**
To simplify, we can move all terms involving \( P \) to one side and all terms involving \( p \) to the other side:
\[ 8P - 3P = 9p - 3p \]
This simplifies to:
\[ 5P = 6p \]

3. **Find the ratio of the cost of one pen to the cost of one pencil:**
We can express \( P \) in terms of \( p \):
\[ \frac{P}{p} = \frac{6}{5} \]
Therefore, the ratio of the cost of one pen to the cost of one pencil is:
\[ P : p = 6 : 5 \]

### Conclusion:
The ratio of the cost of one pen to the cost of one pencil is \( 6 : 5 \).