A sea turtle is 850 meters below sea level. It swims up 165 meters and then descends 165 meters. What integer represents its position, and what is its net change in position?

Step-by-step solution

1. 1

   Turn the words "below sea level" into a signed number. Sea level is the zero of the scale, up is positive and down is negative, so "850 metres below sea level" is the integer

   $-850$

   Choosing this sign convention first is what makes the rest of the problem pure addition.

2. 2

   Add for the upward leg. Rising $165$ m means adding a positive number:

   $-850+165=-685$

   The turtle is now $685$ m below sea level — still negative, because it did not rise far enough to reach the surface.

3. 3

   Subtract for the downward leg. Descending $165$ m means adding $-165$:

   $-685-165=-850$

   So the turtle is back where it started.

4. 4

   Separate "position" from "change in position". These are two different quantities and the wording of the question mixes them:

   $\text{final position}=-850\ \text{m},\qquad \text{net change}=+165+(-165)=0\ \text{m}$

   The integer describing where the turtle is is $-850$; the integer describing how much its position changed is $0$. Answering $-850$ to the second question is the standard mistake here.

5. 5

   Check with the additive-inverse shortcut. $165$ and $-165$ are additive inverses, so their sum is $0$ and the starting value passes through unchanged:

   $-850+\bigl(165+(-165)\bigr)=-850+0=-850$

   This is the associativity check — regrouping the two moves first gives the same $-850$, confirming both answers at once.