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Question 131 **pts**

Morgan’s office, shown in the diagram, is **10 miles** from his home. The question marks represent possible locations of a pizza parlor, which is *x* miles from Morgan’s home.

On Fridays Morgan treats himself to pizza for lunch, so over the course of the day he drives from his home to work, from work to the pizza parlor, back to work, then from work back to his home at the end of the day. The day’s trip is a total of **30 miles**.

Indicate the **shortest possible distance** from the pizza parlor to Morgan's home.

To solve the problem, we need to minimize the distance from Morgan's home to the pizza parlor, given the total distance he drives in a day. Here's a breakdown of the situation:

### Information provided:
- Morgan's home to

Morgan’s office, shown in the diagram, is 10 miles from his home. The question marks represent possible locations of a pizza parlor, which is x miles from Morgan’s home.
On Fridays Morgan treats himself to pizza for lunch, so over the course of the day he drives from his home to work, from work to the pizza parlor, back to work, then from work back to his home at the end of the day. The day’s trip is a total of 30 miles.
Indicate the shortest possible distance from the pizza parlor to Morgan's home.

Solve a distance minimization problem where Morgan drives a total of 30 miles in a day, including a visit to a pizza parlor. Learn how to apply algebra and the triangle inequality to find the shortest possible distance from Morgan's home to the pizza parlor. Suitable for students in Grades 8-10.

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