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Answer :
Let's solve the problem step-by-step:
1. Calculate the Percent Increase for Iliana's Grade:
- Iliana's initial grade: 65
- Iliana's final grade: 86
To find the percent increase, we first calculate how much Iliana's grade increased:
[tex]\[
\text{Increase} = \text{Final Grade} - \text{Initial Grade} = 86 - 65 = 21
\][/tex]
Next, we find the percent increase:
[tex]\[
\text{Percent Increase} = \left(\frac{\text{Increase}}{\text{Initial Grade}}\right) \times 100 = \left(\frac{21}{65}\right) \times 100 \approx 32.31\%
\][/tex]
2. Calculate the Percent Increase for Fiona's Grade:
- Fiona's initial grade: 70
- Fiona's final grade: 80
First, calculate the increase in Fiona's grade:
[tex]\[
\text{Increase} = \text{Final Grade} - \text{Initial Grade} = 80 - 70 = 10
\][/tex]
Then, calculate the percent increase:
[tex]\[
\text{Percent Increase} = \left(\frac{\text{Increase}}{\text{Initial Grade}}\right) \times 100 = \left(\frac{10}{70}\right) \times 100 \approx 14.29\%
\][/tex]
3. Calculate the Difference Between the Percent Increases:
Now, we find the difference between Iliana's and Fiona's percent increases:
[tex]\[
\text{Difference} = 32.31\% - 14.29\% \approx 18\%
\][/tex]
4. Conclusion:
The difference between the approximate percent increases for Iliana's and Fiona's grades, rounded to the nearest whole number, is 18 percent.
The correct answer is 18 percent.
1. Calculate the Percent Increase for Iliana's Grade:
- Iliana's initial grade: 65
- Iliana's final grade: 86
To find the percent increase, we first calculate how much Iliana's grade increased:
[tex]\[
\text{Increase} = \text{Final Grade} - \text{Initial Grade} = 86 - 65 = 21
\][/tex]
Next, we find the percent increase:
[tex]\[
\text{Percent Increase} = \left(\frac{\text{Increase}}{\text{Initial Grade}}\right) \times 100 = \left(\frac{21}{65}\right) \times 100 \approx 32.31\%
\][/tex]
2. Calculate the Percent Increase for Fiona's Grade:
- Fiona's initial grade: 70
- Fiona's final grade: 80
First, calculate the increase in Fiona's grade:
[tex]\[
\text{Increase} = \text{Final Grade} - \text{Initial Grade} = 80 - 70 = 10
\][/tex]
Then, calculate the percent increase:
[tex]\[
\text{Percent Increase} = \left(\frac{\text{Increase}}{\text{Initial Grade}}\right) \times 100 = \left(\frac{10}{70}\right) \times 100 \approx 14.29\%
\][/tex]
3. Calculate the Difference Between the Percent Increases:
Now, we find the difference between Iliana's and Fiona's percent increases:
[tex]\[
\text{Difference} = 32.31\% - 14.29\% \approx 18\%
\][/tex]
4. Conclusion:
The difference between the approximate percent increases for Iliana's and Fiona's grades, rounded to the nearest whole number, is 18 percent.
The correct answer is 18 percent.
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