The amount you pay for a car is not usually the "sticker price," which may be the starting price. The price of a car was reduced by $300 from the sticker price, increased by $900 for additional features, and then reduced by $600 by the dealer. What integer represents the total change in price with respect to the sticker price? Use a number line to represent the change from the sticker price.
Question content area bottom
Part 1
What integer represents the total change in price with respect to the sticker price?
The integer
enter your response here represents the total change in price.
Part 2
Use a number line to represent the change from the sticker price.
Part 1:
The total change in price with respect to the sticker price can be calculated by adding the reductions and the increase.
Reduction = -$300 + (-$600) = -$900
Increase = +$900
Total change = Reduction + Increase = -$900 + $900 = $0
Therefore, the integer that represents the total change in price with respect to the sticker price is 0.
Part 2:
The number line representing the change from the sticker price would have two arrows, one pointing to the left and one pointing to the right, both starting from the sticker price position. The arrow pointing to the left would represent the reduction of $300 and $600, while the arrow pointing to the right would represent the increase of $900. However, since the total change in price is 0, the two arrows would cancel each other out and the final position on the number line would be the same as the sticker price position.
Part 1:
To find the total change in price with respect to the sticker price, we need to add up all the changes.
Let's consider the sticker price as the starting point and represent it as 0.
The price of the car was reduced by $300. So, we move 300 units to the left on the number line.
0 - 300 = -300
Then, the price was increased by $900 for additional features. So, we move 900 units to the right on the number line.
-300 + 900 = 600
Finally, the dealer reduced the price by $600. So, we move 600 units to the left on the number line.
600 - 600 = 0
We end up back at the sticker price, so the total change in price is 0.
Therefore, the integer that represents the total change in price with respect to the sticker price is 0.
Part 2:
On the number line, the changes can be represented as follows:
Starting from the sticker price (0), we move 300 units to the left (-300) to represent the $300 reduction.
Then, from -300, we move 900 units to the right (600) to represent the $900 increase.
Finally, from 600, we move 600 units to the left (0) to represent the $600 reduction by the dealer.
The number line would look like this:
-300 0 600
--------|---------|----|----------> Number Line
So, the changes are represented on the number line from -300 to 600.
Part 1:
To find the total change in price with respect to the sticker price, we need to calculate the net change after all the given changes. Let's break down the problem step by step:
1. The price of the car was reduced by $300 from the sticker price. So, we subtract $300 from the sticker price.
2. Then, the price was increased by $900 for additional features. So, we add $900 to the price after the first reduction.
3. Finally, the price was reduced by $600 by the dealer. So, we subtract $600 from the price after the second addition.
To find the total change in price, we add the three changes together: $300 (initial reduction) + $900 (additional features) - $600 (dealer reduction).
This gives us a net change of $600. However, to represent the change as an integer, we consider positive values as increases and negative values as reductions. Since the net change in this case is a reduction, the integer that represents the total change is -600.
Answer: The integer -600 represents the total change in price with respect to the sticker price.
Part 2:
To represent the change from the sticker price using a number line, we can place the sticker price at 0 on the number line, and then mark the changes accordingly.
Let's assume the sticker price is represented by 0 on the number line. The first reduction of $300 moves us to the left (negative side) by 300 units. We mark this point on the number line.
Next, we add $900 for additional features. Since it's an increase, we move to the right (positive side) by 900 units from the previous point.
Finally, we subtract $600 by the dealer. Since it's a reduction, we move to the left (negative side) by 600 units from the previous point.
The final point on the number line would represent the new price after all the changes.
Answer: The number line representation would show the sticker price at 0, a point at -300 (after the first reduction), a point at 600 (after the additional features), and a final point at 0 (after the dealer reduction). Note that the position of each point represents the change relative to the sticker price.