The overall average grade of a math course is based on homework (10 %) , quizzes (40 %) , and tests (50 %) . Ted has a 90 average for howework , 81 for quizzes , and 85 for tests . What is his overall average ?

Options

A. 83
B. 84
C. 85
D. 86

Explanation

To find Ted's overall average grade in the math course, we will use the concept of weighted averages. The overall average is calculated based on the weights assigned to homework, quizzes, and tests.

### Step-by-Step Solution:

1. **Identify the weights and averages**:
- Homework: 10% (weight = 0.1), Average = 90
- Quizzes: 40% (weight = 0.4), Average = 81
- Tests: 50% (weight = 0.5), Average = 85

2. **Calculate the weighted contribution of each component**:
- For Homework:
\[ \text{Weighted Homework} = 0.1 \times 90 = 9 \]
- For Quizzes:
\[ \text{Weighted Quizzes} = 0.4 \times 81 = 32.4 \]
- For Tests:
\[ \text{Weighted Tests} = 0.5 \times 85 = 42.5 \]

3. **Sum the weighted contributions**:
\[ \text{Overall Average} = \text{Weighted Homework} + \text{Weighted Quizzes} + \text{Weighted Tests} \]
\[ \text{Overall Average} = 9 + 32.4 + 42.5 = 83.9 \]

4. **Round the overall average**:
- Rounding 83.9 gives us approximately 84.

### Final Answer:
Ted's overall average is **84**.