Question
I'm studying for my math final and I'm having trouble understanding how to solve a problem where someone's score increases from one value to another. Can you show me a similar problem and the solution?
Answers
GPT-4o mini
Sure! Let's work through a problem step by step.
**Problem:**
A student scores 75 points on their first test. After studying hard, they take a second test and score 88 points. What is the increase in the student's score from the first test to the second test? Also, what percentage increase did the student achieve?
**Solution:**
1. **Calculate the increase in score:**
To find the increase in score, subtract the first score from the second score:
\[
\text{Increase} = \text{Score on second test} - \text{Score on first test}
\]
\[
\text{Increase} = 88 - 75 = 13 \text{ points}
\]
2. **Calculate the percentage increase:**
To find the percentage increase, you can use the formula:
\[
\text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Original Score}} \right) \times 100
\]
Here, the original score is the score on the first test (75 points).
Substitute the values into the formula:
\[
\text{Percentage Increase} = \left( \frac{13}{75} \right) \times 100
\]
\[
\text{Percentage Increase} \approx 17.33\%
\]
So, the student's score increased by **13 points**, and the percentage increase in their score is approximately **17.33%**.
By following these steps, you can approach similar problems where you need to analyze changes in scores or values! Let me know if you have more questions or need additional examples!
**Problem:**
A student scores 75 points on their first test. After studying hard, they take a second test and score 88 points. What is the increase in the student's score from the first test to the second test? Also, what percentage increase did the student achieve?
**Solution:**
1. **Calculate the increase in score:**
To find the increase in score, subtract the first score from the second score:
\[
\text{Increase} = \text{Score on second test} - \text{Score on first test}
\]
\[
\text{Increase} = 88 - 75 = 13 \text{ points}
\]
2. **Calculate the percentage increase:**
To find the percentage increase, you can use the formula:
\[
\text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Original Score}} \right) \times 100
\]
Here, the original score is the score on the first test (75 points).
Substitute the values into the formula:
\[
\text{Percentage Increase} = \left( \frac{13}{75} \right) \times 100
\]
\[
\text{Percentage Increase} \approx 17.33\%
\]
So, the student's score increased by **13 points**, and the percentage increase in their score is approximately **17.33%**.
By following these steps, you can approach similar problems where you need to analyze changes in scores or values! Let me know if you have more questions or need additional examples!