Charmaine is looking at the rental car prices for Get You There Rental Car Company. The cost is based on how many miles you plan to drive the rental car. Use the list of rental prices to answer the questions 1- 5.
Miles Cost
200 $80
600 $120
1000 $160
1400 $200
1800 $320
1) Describe the relationship between the cost of the rental car and the miles.
2) Write a linear equation to represent the relationship between the cost and the miles.
3) Estimate the cost of driving the rental car for 1200 miles.
4) Predict the cost of driving the rental car for 2400 miles.
5) With $500, what is the maximum number of miles that you can drive the rental car?
These questions seem so simple to me but I got them all wrong... Can someone please help me?
1)This looks like a strong positive linear relationship between the cost of the rental car and the miles (as the mileage increases, so does the cost).
2)Linear equation:
predicted y = 36 + 0.14x
x = miles
y = cost
3)Substitute 1200 for x (miles) and solve for predicted y (cost).
4)Substitute 2400 for x (miles) and solve for predicted y (cost).
5)Substitute 500 for y (cost) and solve for x (miles).
I hope this will help get you started.
1) Well, the relationship between the cost of the rental car and the miles seems to be that the cost increases as the number of miles driven increases. It's like the rental car company is saying, "The more you drive, the more it'll cost you. Drive it like you rented it!"
2) To represent this relationship in a linear equation, we can use the classic formula: y = mx + b. In this case, y represents the cost, x represents the miles, m represents the rate of increase (slope), and b represents the initial cost.
To find the slope, we can choose any two points from the data. Let's use (200, $80) and (1000, $160):
m = (160 - 80) / (1000 - 200)
m = 80 / 800
m = 0.1
Now, let's find the initial cost (y-intercept) by substituting one of the points into the equation:
80 = 0.1 * 200 + b
80 = 20 + b
b = 60
So the linear equation that represents the relationship is: y = 0.1x + 60.
In a way, you can think of it as "The cost of the rental car is equal to 10 cents per mile, plus a base fee of $60."
3) To estimate the cost of driving the rental car for 1200 miles, we can plug the value of x = 1200 into the equation and solve for y:
y = 0.1 * 1200 + 60
y = 120 + 60
y = $180
So the estimated cost for driving 1200 miles would be $180.
4) To predict the cost of driving the rental car for 2400 miles, we can again use the equation:
y = 0.1 * 2400 + 60
y = 240 + 60
y = $300
The predicted cost for driving 2400 miles would be $300.
5) With $500, let's find out the maximum number of miles you can drive the rental car by substituting y = 500 into the equation and solving for x:
500 = 0.1x + 60
440 = 0.1x
x = 4400
So, you can drive a maximum of 4400 miles with $500. Just remember, if you hear a loud "ka-ching" after every mile, it means you're getting closer to your limit!
1) The relationship between the cost of the rental car and the miles is that as the number of miles increases, the cost of the rental car also increases.
2) To write a linear equation to represent the relationship between the cost and the miles, we can find the equation of the line that passes through two points on the graph. Let's take the points (200, $80) and (1000, $160).
Using the slope formula:
slope = (change in cost) / (change in miles)
= ($160 - $80) / (1000 - 200)
= $80 / 800
= $0.10
Using the point-slope form of a linear equation:
y - y1 = m(x - x1), where (x1, y1) is a point on the line
Using point (200, $80):
y - 80 = 0.10(x - 200)
y - 80 = 0.10x - 20
y = 0.10x + 60
So, the linear equation representing the relationship between the cost and the miles is y = 0.10x + 60, where y is the cost in dollars and x is the number of miles driven.
3) To estimate the cost of driving the rental car for 1200 miles, we can substitute x = 1200 into the linear equation:
Cost = 0.10(1200) + 60 = $180
Therefore, the estimated cost of driving the rental car for 1200 miles is $180.
4) To predict the cost of driving the rental car for 2400 miles, we can substitute x = 2400 into the linear equation:
Cost = 0.10(2400) + 60 = $300
Therefore, the predicted cost of driving the rental car for 2400 miles is $300.
5) To find the maximum number of miles that can be driven with $500, we can substitute y = 500 into the linear equation and solve for x:
500 = 0.10x + 60
0.10x + 60 = 500
0.10x = 440
x = 4400
Therefore, with $500, the maximum number of miles that can be driven is 4400 miles.
Of course! I'm here to help you understand how to solve these questions.
1) To describe the relationship between the cost of the rental car and the miles, we can observe that as the number of miles increases, the cost also increases. In other words, there is a positive correlation between the cost and the number of miles.
2) To write a linear equation to represent this relationship, we need to find the slope and the y-intercept. The slope can be calculated by finding the change in cost divided by the change in miles. Let's use the first two data points: (200, $80) and (600, $120).
Slope = (change in cost) / (change in miles) = ($120 - $80) / (600 - 200) = $40 / 400 = $0.1 per mile.
Now, we can use the point-slope form of a linear equation, where the slope is 0.1 and we can choose any point to substitute. Let's use (200, $80):
cost - $80 = 0.1(miles - 200)
This equation can be simplified as:
cost = 0.1miles - 20.
3) To estimate the cost of driving the rental car for 1200 miles, we can substitute 1200 for "miles" in the equation we obtained in step 2:
cost = 0.1(1200) - 20 = $120 - 20 = $100.
Therefore, the estimated cost of driving the rental car for 1200 miles is $100.
4) To predict the cost of driving the rental car for 2400 miles, we can substitute 2400 for "miles" in the same equation:
cost = 0.1(2400) - 20 = $240 - 20 = $220.
Therefore, the predicted cost of driving the rental car for 2400 miles is $220.
5) To determine the maximum number of miles you can drive the rental car with $500, we can rearrange the equation from step 2 to solve for "miles":
0.1miles = cost + 20.
miles = (cost + 20) / 0.1.
Substituting $500 for "cost":
miles = ($500 + 20) / 0.1 = $520 / 0.1 = 5200.
Therefore, with $500, you can drive the rental car up to a maximum of 5200 miles.
I hope this helps! Let me know if you have any further questions.