On the first test of the semester, Barbara scored a 60. On the first test of the semester, Barbara scored a 75. By what percent did Barbara's score improve?

Options

A. 0.15
B. 0.18
C. 0.2
D. 0.25

Answer

To find the percentage improvement in Barbara's score from the first test to the second test, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final Scores**:
- Initial score (first test) = 60
- Final score (second test) = 75

2. **Calculate the Difference in Scores**:
- Difference = Final score - Initial score
- Difference = 75 - 60 = 15

3. **Use the Percentage Change Formula**:
- The formula for percentage change is:
\[ \text{Percentage Change} = \left( \frac{\text{Difference}}{\text{Initial Value}} \right) \times 100 \]
- Here, the initial value is 60.

4. **Substitute the Values into the Formula**:
- Substitute the difference and the initial value into the formula:
\[ \text{Percentage Change} = \left( \frac{15}{60} \right) \times 100 \]

5. **Simplify the Fraction**:
- Simplifying \( \frac{15}{60} \) gives:
\[ \frac{15}{60} = \frac{1}{4} \]

6. **Calculate the Percentage**:
- Now multiply by 100:
\[ \text{Percentage Change} = \frac{1}{4} \times 100 = 25 \]

7. **Conclusion**:
- Therefore, Barbara's score improved by **25%**.