Question

Roberto is shopping in a large department store with many floors. He

enters the store on the middle floor from a skyway and immediately
goes to the credit department. After making sure his credit is good, he
goes up three floors to the housewares department. Then he goes down
five floors to the children's department. Then he goes up six floors to the
TV department. Finally, he goes down ten floors to the main entrance of
the store, which is on the first floor, and leaves to go to another store
down the street. How many floors does the department store have?

Answer 1

To determine the number of floors in the department store, we follow Roberto's path from the middle floor and track his movements to the defined exits. Calculating his steps reveals that the middle floor is the seventh floor, thus the department store has a total of 13 floors.

Step-by-step explanation:

To determine the total number of floors in the department store, let's follow Roberto's journey starting from the middle floor where he enters. First, he goes to the credit department on the same floor he entered. Then he goes up three floors to the housewares department, then down five floors to the children's department, followed by going up six floors to the TV department. Finally, he descends ten floors to exit the department store through the main entrance on the first floor.

Let's denote the middle floor as M. After these moves, Roberto is at the first floor (F). Roberto's journey can be summarized as follows:

Middle floor (Entrance) = M

M + 3 (Housewares)

M + 3 - 5 (Children's)

M + 3 - 5 + 6 (TV Department)

M + 3 - 5 + 6 - 10 = 1 (Main Entrance)

By simplifying, we find M ends up being the fourth floor of the department store:

M + 3 - 5 + 6 - 10 = 1

M - 6 = 1

M = 1 + 6

M = 7

Since M is the middle floor and it is the seventh floor, the department store must then have 13 floors in total (six floors above and six floors below the middle).