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Question

# In many buildings, particularly outside of the United States, the ground floor of a building is labeled as G or Lobby. The first floor of the building is one floor above the ground floor. The building pictured has a lobby, 10 floors of offices, and 4 floors of garage below the lobby. a. Melanie has an office on the 9th floor and parks on the 3rd floor below the ground floor. Taylor and Cecelia are determining how many floors Melanie must go up from her car to reach her office. Taylor represents the 9th floor as 9 and the 3rd floor below ground as -3. Therefore, since 9 - 3 = 6, Melanie traveled 6 floors to get from her car to her office. Cecelia says that the ground floor to the 9 th floor is 9 floors, and from the ground floor to the 3 rd garage level is 3 floors. Melanie traveled |9| + |-3| = 9 + 3 = 12 floors. Who is correct? Explain your reasoning. b. Caleb parks his car on the 2 nd floor below ground and works on the 7th floor. How many floors must he go up from his car to reach his office? c. Lucinda is working on the 8th floor. At lunch, she goes to her car on the 4 th floor below ground, and then back up to the lobby. How many total floors does Lucinda travel? d. If Damon goes from his office on the 10th floor to a meeting on the 5th floor, how many floors does he travel and in which direction?

Solution

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a) Taylor is incorrect since 6 floors below Melanie's office on the 9th floor would be the 3rd floor above the lobby, not the 3rd floor below the lobby. To find the total number of floors, you need to find the number of floors from the lobby to the 9th floor above the lobby, the number of floors from the 3rd garage level to the lobby, and then add so Cecilia is correct.

b) The 7th floor above the lobby is represented by the number 7. The 2nd floor below ground is represented by the number $-2$. The number of floors Caleb must go is then $|7|+|-2|=7+2=9$.

c) The 8th floor above the lobby is represented by the number 8. The 4th floor below ground is represented by the number $-4$. The number of floors that Lucina must go is then $|8|+|-4|+|-4|=8+4+4=16$. Note that we need to add $|-4|$ twice since she goes from the lobby down to the 4th floor below ground level and then goes back up the four floors to get back to the lobby.

d) The 10th floor is represented by the number 10 and the 5th floor is represented by the number 5. Since both numbers are positive, we need to subtract the two numbers to find how many floors Damon must travel. He will then travel $10-5=5$ floors down.

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