Use a number line to help represent the situation from the exercise. Recall how to describe changes on a number line using absolute values.
Mrs. Jones's Offer: -240 Mr. Beliz's Offer: -248 Conclusion: Mrs. Jones's lessons are the better deal. See solution.
Practice makes perfect
We want to determine which teacher offers the better deal for Samantha. First, let's take a look at the two different offers from the guitar teachers.
Teacher
Cost per Lesson
Number of Lessons to Learn the Song
Mrs. Jones
$80
3
Mr. Beliz
$62
4
We can use a number line to find out how much Samantha has to pay for each offer.
Mrs. Jones's offer
Let's start with Mrs. Jones's offer. We know that Mrs. Jones requires 3 lessons to teach Samantha her favorite song. That means she will have to pay $80 3 times. Let's list the steps we will follow to create a number line for this situation.
First, we start at 0.
Next, we move 80 units to the left. This represents the first lesson.
Then, we move 80 more units to the left for the second lesson.
Finally, we move 80 units to the left one more time to represent the last lesson needed to learn the song.
Let's mark these steps on the number line.
As we can see from the graph, the sum of - 80, -80, and -80 describes the situation from the exercise. Let's write an expression to represent the cost of learning the song from Mrs. Jones.
Mrs. Jones's Offer: (-80)+(-80)+(-80)
We will add the three integers to solve the expression. We can solve it exactly as we would solve for two integers. Notice that we are adding integers with the samesigns, all negative. This means that we will add the absolute values of the integers. Let's do it!
Keep in mind that we moved three times to the left of 0 on the number line. This means that the result is negative, and we can say that the integer that represents the amount of money Mrs. Jones's charges is -240.
Mr. Beliz's offer
Now let's focus on Mr. Beliz's offer. Let's make another list of the steps we we will follow to create a number line for this situation.
First, we start at 0.
Next, we move 62 units to the left. We do this to represent the first lesson.
Then, we move 62 more units to the left for the second lesson.
Then, we move 62 units to the left again to represent the third lesson.
Finally, we move 62 units to the left one more time. This represents the last lesson needed to learn the song.
Let's mark these steps on the number line.
The graph suggests that the sum of - 62, -62, -62, and -62 describes the situation from the exercise. Let's write these integers as an addition expression to represent the amount of money that Mr. Beliz charges to learn the song.
Mr. Beliz's Offer: (-62)+(-62)+(-62)+(-62)
We can add the integers together to find how much money Samantha will have after learning the songs. Notice that these integers have the same signs again, four negative. Let's add the absolute values of the integers.
We moved four times to the left of 0 on the number line. This means that the result is negative, and we can say that the integer that represents the amount of money Mr. Beliz's charges is -248.
Comparison
Finally, let's compare costs of each set of lessons.
Cost of Mrs. Jones's Lessons:& $240
Cost of Mr. Beliz's Lessons:& $248
If we compare the two offers, we can say that Mrs. Jones offers a better deal because Samantha will have to pay less to learn the song.
