https://file.aiquickdraw.com/mathbot/file/1729485738544lfa1uo4v.jpg

To solve the problem, let's break it down step by step:

### Known scores:
Thao's current scores on six exams are:
- 78, 83, 44, 89, 78, 89

The score of 44 will be replaced by the score on a "make-up" exam, and Thao wants to achieve an overall average (mean) of **80**.

### Step 1: Calculate the current total of the other 5 scores.
First, sum the scores excluding the one Thao will replace (44):
\[
78 + 83 + 89 + 78 + 89 = 417
\]

### Step 2: Set up the equation.
Let \( x \) be the score that Thao must get on the make-up exam to achieve an overall average of 80. Since the new total score will include \( x \) instead of 44, we can set up the equation as follows:

\[
\text{New total score} = 417 + x
\]
The total number of exams is still 6, so the equation for the average is:
\[
\frac{417 + x}{6} = 80
\]

### Step 3: Solve for \( x \).
Multiply both sides by 6:
\[
417 + x = 480
\]
Now, subtract 417 from both sides:
\[
x = 480 - 417
\]
\[
x = 63
\]

### Conclusion:
Thao must score **63** on the make-up exam to get an overall average of 80.

Do you have any questions or need further explanation? Here are some related questions to consider:

1. How do you calculate the mean for a set of numbers?
2. What would happen if Thao scored higher or lower than 63 on the make-up exam?
3. How is the mean affected by replacing just one score in a set of numbers?
4. What if Thao needed an average higher than 80? How would the solution change?
5. What is the impact of a very low score (like 44) on the overall average?

**Tip:** When working with averages, replacing an outlier score can significantly change the result, especially in smaller data sets.

Thao earned the following scores on her six management exams last semester: 78, 83, 44, 89, 78, 89. Thao has a chance to replace her score of 44 by taking a 'make-up' exam. What must she score on the make-up exam to get an overall average of 80?

Learn how to calculate the score Thao must achieve on her make-up exam to replace a low score and reach an overall average of 80. With clear steps, this problem covers key concepts such as averages and basic algebra. Ideal for students in Grades 6-9.

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