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Use a number line to help represent the given situations. Recall what we know about opposites.
See solution.
We want to find out which of the five given situations can be represented by the opposite of 80. To do so, we will use a number line and check if the given integer is the opposite of 80. We will consider the situations one at a time. Let's begin with the first one. An airplane descends 80 m. We will use a number line to show this situation. Let's use 0 to represent the initial position of the airplane and mark the distance it descends. Keep in mind that when an objects descends, we move to the left on the number line.
An elevator ascends 80 m. Once again, we will use a number line to show the situation. This time, however, we will move to the right on the number line because the elevator ascends, or goes up.
The integer that represents the situation is 80. We know that the number we found is not the opposite of 80. Now, we can consider the third situation. The cost of a train ticket drops by $80. To represent this situation on a number line, we will mark 0 as the initial price of the train ticket. Keep in mind that when the price drops, we move to the left on the number line. Let's take a look.
We can see that the integer representing this situation is -80, and as we already stated, it is the opposite of 80. With this out of the way, we can move on to the fourth situation. You remove 80 songs from an MP3 player. In this instance, we will use 0 to represent the initial number of songs on the MP3 player. Notice that when we remove songs, we move to the left on the number line.
Just like in the previous situation we considered, the integer that represents this situation is -80, and it is the opposite of 80. Now we can move to the fifth situation given in the exercise. Suzy's grandmother is 80 years old. Finally, let's mark the fifth situation on a number line. We will use 80 to represent the age of Suzy's grandma.
Notice that since the age of Suzy's grandmother does not change, it is 80, which is not the opposite of 80. With this information, we are ready to mark all situations that can be represented with an integer that is the opposite of 80. &✓ An airplane descends 80 m. &* An elevator ascends 80 m. &✓ The cost of a train ticket drops by $80 &✓ You remove 80songs from an MP3 player. &* Suzy's grandmother is 80 years old.
