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To solve this problem, we will use the **midpoint formula** to approximate the cost in 1987.

### Given:
- In 1983, the cost of tuition and fees was \$5059.
- In 1991, the cost of tuition and fees was \$9987.

The midpoint formula is used to find the middle value between two points on a line, which in this case can approximate the cost in 1987. The formula is:

\[
\text{Midpoint} = \frac{x_1 + x_2}{2}
\]

Here, $ x_1 $ is the cost in 1983 (\$5059), and $ x_2 $ is the cost in 1991 (\$9987).

Let me calculate this value for you.Using the midpoint formula, the approximate cost of tuition and fees in 1987 was **$7,523**.

Do you have any further questions or would you like a more detailed explanation?

Here are five related questions you might find useful:
1. How is the midpoint formula applied to other real-world scenarios?
2. What is the slope of the line segment between 1983 and 1991?
3. How can we predict tuition costs for years beyond 1991 using this data?
4. What other methods can be used to estimate the cost for years between two known values?
5. How does the linear model compare to actual historical tuition increases?

**Tip**: The midpoint formula is often used to estimate averages between two data points, especially in situations where linear change is assumed, such as here with the tuition costs.

The graph depicts the growth in costs using a line segment. Use the midpoint formula to approximate the cost during the year 1987. The approximate cost during the year 1987 was ___?

Learn how to use the midpoint formula to estimate the 1987 tuition costs at private colleges based on the average annual costs in 1983 and 1991. This method is suitable for students in Grades 9-10 and covers the midpoint formula for linear estimation.

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