A local restaurant serves cold Gazpacho soup.
One day, the soup was served at 65 degrees Fahrenheit. Each following day, the soup was served either 8 degrees warmer or 10 degrees colder than the previous day. What is the lowest temperature the soup could be served at?

Let's define the situation step by step:

- On day 1, the soup was served at 65°F.
- Each day afterward, the temperature either increases by 8°F or decreases by 10°F compared to the previous day.

To find the lowest possible temperature, we need to keep decreasing the temperature as much as possible. This means we will continuously choose the option of decreasing by 10°F.

If we decrease by 10°F every day, the temperature sequence becomes:

\[
65 - 10 = 55
\]
\[
55 - 10 = 45
\]
\[
45 - 10 = 35
\]
\[
35 - 10 = 25
\]
\[
25 - 10 = 15
\]
\[
15 - 10 = 5
\]
\[
5 - 10 = -5
\]

Thus, the lowest possible temperature is **-5°F**.

### Do you have any questions, or would you like more details on how I derived this solution?

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Here are 5 related questions for further exploration:

1. How would the result change if the temperature could only increase by 5°F instead of 8°F?
2. What is the highest temperature the soup could be served at if we always chose to increase it?
3. How many days would it take to reach the lowest temperature if a random mix of changes (both increases and decreases) was applied?
4. Can the temperature ever return to 65°F after a few days of increases and decreases?
5. What if there were an additional rule that the temperature cannot drop below 0°F?

**Tip:** Always pay attention to patterns when dealing with sequences of changes, as they can help predict future outcomes more easily!

A local restaurant serves cold Gazpacho soup. One day, the soup was served at 65 degrees Fahrenheit. Each following day, the soup was served either 8 degrees warmer or 10 degrees colder than the previous day. What is the lowest temperature the soup could be served at?

This problem explores an arithmetic sequence involving temperature changes where a soup's temperature either increases by 8°F or decreases by 10°F each day. Learn how to find the lowest possible temperature, including key concepts of arithmetic sequences and negative numbers. Suitable for students in Grades 5-7.

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