To determine what percentage of the remaining 225 points Daniella must earn to achieve an average of 90%, we will follow a step-by-step approach.
1. Calculate the total possible points by the end of the term:
- Initial points possible: 700
- Remaining points: 225
- Total possible points: [tex]\(700 + 225 = 925\)[/tex]
2. Calculate the points needed to have an average of 90%:
- Desired average: 90% or 0.90
- Desired total score: [tex]\(0.90 \times 925\)[/tex]
[tex]\[
\text{Desired total score} = 0.90 \times 925 = 832.5
\][/tex]
3. Determine the points Daniella currently has and how many more she needs:
- Current points: 598
- Points needed: [tex]\(832.5 - 598\)[/tex]
[tex]\[
\text{Points needed} = 832.5 - 598 = 234.5
\][/tex]
4. Calculate the percentage of the remaining 225 points that Daniella must earn:
- Points needed: 234.5
- Total remaining points: 225
- Percentage needed: [tex]\(\frac{234.5}{225} \times 100\)[/tex]
[tex]\[
\text{Percentage needed} = \frac{234.5}{225} \times 100 \approx 104.22\%
\][/tex]
So, Daniella needs to earn approximately 104.22% of the remaining 225 points to achieve an average of 90%. This means it is not possible for Daniella to get an average of 90% by the end of the term, as it is impossible to score more than 100% of the remaining points.
