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Answer :
Sure, let's break this down step-by-step:
1. Identify Initial and Final Grades:
- Iliana's grades increased from 65 to 86.
- Fiona's grades increased from 70 to 80.
2. Calculate the Increase in Grades:
- For Iliana: [tex]\( 86 - 65 = 21 \)[/tex]
- For Fiona: [tex]\( 80 - 70 = 10 \)[/tex]
3. Calculate the Percentage Increase:
- Iliana's Percentage Increase:
[tex]\[
\left( \frac{21}{65} \right) \times 100 \approx 32.31\%
\][/tex]
- Fiona's Percentage Increase:
[tex]\[
\left( \frac{10}{70} \right) \times 100 \approx 14.29\%
\][/tex]
4. Find the Difference Between the Percentage Increases:
- Difference = [tex]\( 32.31\% - 14.29\% \approx 18.02\% \)[/tex]
5. Round the Difference to the Nearest Whole Number:
- Rounded Difference = 18%
So, the difference between the approximate percent increases, rounded to the nearest whole number, is [tex]\( 18\% \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{18\%} \][/tex]
1. Identify Initial and Final Grades:
- Iliana's grades increased from 65 to 86.
- Fiona's grades increased from 70 to 80.
2. Calculate the Increase in Grades:
- For Iliana: [tex]\( 86 - 65 = 21 \)[/tex]
- For Fiona: [tex]\( 80 - 70 = 10 \)[/tex]
3. Calculate the Percentage Increase:
- Iliana's Percentage Increase:
[tex]\[
\left( \frac{21}{65} \right) \times 100 \approx 32.31\%
\][/tex]
- Fiona's Percentage Increase:
[tex]\[
\left( \frac{10}{70} \right) \times 100 \approx 14.29\%
\][/tex]
4. Find the Difference Between the Percentage Increases:
- Difference = [tex]\( 32.31\% - 14.29\% \approx 18.02\% \)[/tex]
5. Round the Difference to the Nearest Whole Number:
- Rounded Difference = 18%
So, the difference between the approximate percent increases, rounded to the nearest whole number, is [tex]\( 18\% \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{18\%} \][/tex]
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