A bar graph is drawn to the scale of 1 cm = k units. The length of the bar representing a quantity 405 units is 5.4 cm. Find k.

Options

A. 100
B. 70
C. 80
D. 75

Answer

To solve the problem, we need to find the value of \( k \) given that a bar graph has a scale of 1 cm = \( k \) units, and the length of the bar representing 405 units is 5.4 cm.

### Step-by-Step Solution:

1. **Understand the relationship given in the problem**:
- The scale of the bar graph is \( 1 \text{ cm} = k \text{ units} \).
- The length of the bar representing 405 units is 5.4 cm.

2. **Set up the equation**:
- We know that if 5.4 cm represents 405 units, we can find out how many units are represented by 1 cm.
- Therefore, we can calculate the number of units per cm by dividing the total units by the length in cm:
\[ \text{Units per cm} = \frac{405 \text{ units}}{5.4 \text{ cm}} \]

3. **Calculate the units per cm**:
- To perform the division, we can first eliminate the decimal by multiplying both the numerator and the denominator by 10:
\[ \frac{4050}{54} \]
- Now, we can simplify this fraction:
\[ 4050 \div 54 = 75 \]
- Thus, we find that:
\[ 1 \text{ cm} = 75 \text{ units} \]

4. **Relate this back to \( k \)**:
- Since we have established that \( 1 \text{ cm} = 75 \text{ units} \), and we know from the problem statement that \( 1 \text{ cm} = k \text{ units} \), we can conclude:
\[ k = 75 \]

5. **Final answer**:
- Therefore, the value of \( k \) is:
\[ \boxed{75} \]