To determine Elaine's overall grade average, we'll follow these steps:
1. Calculate the average grade for each component:
- Homework:
Elaine has four homework grades: 76, 84, 100, and 89. To find the average homework grade, we add these grades together and then divide by the number of homework assignments.
[tex]\[
\text{Homework Average} = \frac{76 + 84 + 100 + 89}{4}
\][/tex]
2. Add the homework grades:
[tex]\[
76 + 84 + 100 + 89 = 349
\][/tex]
3. Calculate the homework average:
[tex]\[
\text{Homework Average} = \frac{349}{4} = 87.25
\][/tex]
Rounding to the nearest tenth, we get:
[tex]\[
\text{Homework Average} = 87.2
\][/tex]
4. Quizzes and Exams:
Elaine has three grades for quizzes and exams: 77, 92, and 83. To find the average, we add these grades together and then divide by the number of quizzes and exams.
[tex]\[
\text{Quizzes and Exams Average} = \frac{77 + 92 + 83}{3}
\][/tex]
5. Add the quizzes and exams grades:
[tex]\[
77 + 92 + 83 = 252
\][/tex]
6. Calculate the quizzes and exams average:
[tex]\[
\text{Quizzes and Exams Average} = \frac{252}{3} = 84
\][/tex]
7. Projects:
Elaine has one project grade: 90. Since there's only one grade, the average grade is the grade itself:
[tex]\[
\text{Project Average} = 90
\][/tex]
8. Calculate the overall grade:
The overall grade is a weighted average of the three components. Homework counts for 50% of the grade, quizzes and exams count for 25%, and projects count for the remaining 25%.
[tex]\[
\text{Overall Grade} = (87.2 \times 0.5) + (84 \times 0.25) + (90 \times 0.25)
\][/tex]
9. Calculate each component's contribution:
- Homework:
[tex]\[
87.2 \times 0.5 = 43.6
\][/tex]
- Quizzes and Exams:
[tex]\[
84 \times 0.25 = 21
\][/tex]
- Projects:
[tex]\[
90 \times 0.25 = 22.5
\][/tex]
10. Add these contributions together to obtain the overall grade:
[tex]\[
\text{Overall Grade} = 43.6 + 21 + 22.5 = 87.1
\][/tex]
Thus, Elaine's current grade in the course is:
[tex]\[
\boxed{87.1}
\][/tex]
