To determine which expressions accurately represent Kiana’s movements, we need to break down her journey step-by-step:
1. Starting Point: Kiana is on the 5th floor.
2. First Movement: She goes down 7 floors to the parking garage.
3. Second Movement: She then goes up 2 floors to the hotel lobby.
Let's evaluate each expression:
1. Expression: [tex]\( 5 + 7 + 2 \)[/tex]
- Calculation:
[tex]\[
5 \quad (\text{starting at the 5th floor}) \\
+ 7 \quad (\text{going up 7 floors})
= 12 \quad (\text{now on the 12th floor}) \\
+ 2 \quad (\text{going up 2 more floors})
= 14 \quad (\text{now on the 14th floor})
\][/tex]
- This expression is not correct since Kiana did not go up before she went down.
2. Expression: [tex]\( 5 + (-7) + 2 \)[/tex]
- Calculation:
[tex]\[
5 \quad (\text{starting at the 5th floor}) \\
+ (-7) \quad (\text{going down 7 floors})
= -2 \quad (\text{now on 2 floors below ground}) \\
+ 2 \quad (\text{going up 2 floors})
= 0 \quad (\text{back to the ground floor, which is the lobby})
\][/tex]
- This expression is correct.
3. Expression: [tex]\( (-5) + 7 + 2 \)[/tex]
- Calculation:
[tex]\[
-5 \quad (\text{starting at a hypothetically negative 5th floor}) \\
+ 7 \quad (\text{going up 7 floors})
= 2 \quad (\text{now on the 2nd floor}) \\
+ 2 \quad (\text{going up 2 more floors})
= 4 \quad (\text{now on the 4th floor})
\][/tex]
- This expression is not correct because Kiana starts on the positive 5th floor, not at a negative floor.
4. Expression: [tex]\( 5 + 2 + (-7) \)[/tex]
- Calculation:
[tex]\[
5 \quad (\text{starting at the 5th floor}) \\
+ 2 \quad (\text{going up 2 floors})
= 7 \quad (\text{now on the 7th floor}) \\
+ (-7) \quad (\text{going down 7 floors})
= 0 \quad (\text{back to the ground floor, which is the lobby})
\][/tex]
- This expression is correct because the final position matches the described movements correctly, even though it takes an indirect path.
Therefore, the correct expressions that represent Kiana's real-world situation are:
- [tex]\( 5 + (-7) + 2 \)[/tex]
- [tex]\( 5 + 2 + (-7) \)[/tex]
