Amy hikes down a slope to a lake that is
\[10.2\] meters below the trail. Then Amy jumps into the lake, and swims
\[1.5\] meters down. She wonders what her new height is relative to the trail.
Which of the following equations matches the situation above?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[-10.2+1.5 = \:?\]
A
\[-10.2+1.5 = \:?\]
(Choice B)
\[10.2-1.5 = \:?\]
B
\[10.2-1.5 = \:?\]
(Choice C)
\[-10.2-1.5 =\: ?\]
C
\[-10.2-1.5 =\: ?\]

Amy starts by hiking **10.2 meters down**, which means her position relative to the trail is now at \(-10.2\) meters. After that, she swims **1.5 meters further down** from this point, so her new height should be the sum of both negative distances.

This means the correct equation is:
\[
-10.2 - 1.5 = \: ?
\]

Thus, the correct choice is **Choice C**:
\[
-10.2 - 1.5 = \: ?
\]

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. What would happen if Amy swam back up by 1 meter?
2. How could you represent the situation using a number line?
3. If Amy hiked back up halfway, what would her height relative to the trail be?
4. How does the negative sign affect the calculation?
5. What would Amy’s height be if the lake was 20 meters below the trail?

**Tip:** Negative numbers are used to represent downward movement in situations like this. Always be mindful of how signs affect addition or subtraction.

Amy hikes down a slope to a lake that is 10.2 meters below the trail. Then Amy jumps into the lake and swims 1.5 meters down. She wonders what her new height is relative to the trail. Which of the following equations matches the situation?

Explore how to solve a problem involving negative numbers as Amy hikes 10.2 meters below a trail and swims 1.5 meters further down. Learn the mathematical process of adding negative values, suitable for students in Grades 6-8.

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