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AN ELEVATOR ON THE 10TH FLOOR GOES DOWN 9 FLOORS. THEN IT GOES UP 19 FLOORS, DOWN 3, AND FINALLY DOWN 12.
WHAT FLOOR DOES IT END UP ON? WRITE AN EQUATION TO SHOW HOW YOU FOUND YOUR ANSWER.
Starting on the 10th floor, the elevator goes down 9 floors to the first floor, so it is now on the 1st floor.
Then it goes up 19 floors, bringing it to the 20th floor.
Next, it goes down 3 floors, bringing it to the 17th floor.
Finally, it goes down 12 floors, bringing it to the 5th floor.
Therefore, the elevator ends up on the 5th floor.
Equation: 10 - 9 + 19 -3 -12 = 5
To find the floor where the elevator ends up, we can keep track of the total number of floors it goes up and the total number of floors it goes down.
Starting from the 10th floor:
- The elevator goes down 9 floors, which means it is on the 10th - 9 = 1st floor.
- Then it goes up 19 floors, so it is now on the 1st + 19 = 20th floor.
- Next, it goes down 3 floors, so it is on the 20th - 3 = 17th floor.
- Finally, it goes down 12 floors, which means it ends up on the 17th - 12 = 5th floor.
Therefore, the elevator ends up on the 5th floor.
To represent this step-by-step process using an equation, let's use the variable "x" to represent the starting floor. We will subtract the number of floors that the elevator goes down and add the number of floors that it goes up in each step:
Starting floor: x
After going down 9 floors: x - 9
After going up 19 floors: (x - 9) + 19
After going down 3 floors: ((x - 9) + 19) - 3
After going down 12 floors: (((x - 9) + 19) - 3) - 12
Simplifying the equation:
x - 9 + 19 - 3 - 12 = x - 5
Therefore, the equation to represent the final floor is x - 5, where x represents the starting floor of the elevator.
To find the final floor the elevator ends up on, we need to keep track of its movement from the 10th floor. We can do this by subtracting the number of floors it goes down and adding the number of floors it goes up.
Starting from the 10th floor:
- It goes down 9 floors, so we subtract 9: 10 - 9 = 1
- It goes up 19 floors, so we add 19: 1 + 19 = 20
- It goes down 3 floors, so we subtract 3: 20 - 3 = 17
- It goes down 12 floors, so we subtract 12: 17 - 12 = 5
Therefore, the elevator ends up on the 5th floor.
In equation form, we can represent the elevator's movement as:
10 - 9 + 19 - 3 - 12 = 5