Susan received grades of 78, 93, 82, and 76 on four math exams. What is the lowest score she can receive on her next math exam and have an average of at least 85 on the five exams?

Options

A. `96`
B. `94`
C. `92`
D. `90`

Answer

To find the lowest score Susan can receive on her next math exam to achieve an average of at least 85, we can follow these steps:

### Step 1: Determine the total score needed for an average of 85
To find the total score needed for an average of 85 over 5 exams, we can use the formula for average:

\[ \text{Average} = \frac{\text{Total Score}}{\text{Number of Exams}} \]

Rearranging this gives us:

\[ \text{Total Score} = \text{Average} \times \text{Number of Exams} \]

Substituting the values:

\[ \text{Total Score} = 85 \times 5 = 425 \]

### Step 2: Calculate the sum of the scores from the first four exams
Now, we need to sum the scores from the first four exams:

\[ \text{Scores} = 78 + 93 + 82 + 76 \]

Calculating this gives:

\[ \text{Scores} = 329 \]

### Step 3: Set up the inequality for the fifth exam score
Let \( X \) be the score on the fifth exam. We need the total score from all five exams to be at least 425:

\[ 329 + X \geq 425 \]

### Step 4: Solve for \( X \)
To find the minimum score \( X \), we can rearrange the inequality:

\[ X \geq 425 - 329 \]

Calculating the right side:

\[ X \geq 96 \]

### Conclusion
The lowest score Susan can receive on her next math exam to achieve an average of at least 85 is **96**.