Simple real life math problem to solve..

[moremath]

The problem is the following:

Need to find the average price of X type of used car based on mileage alone.

For this I have gathered the price and mileage of 8 "sold" cars.
Then I got the average of mileage and price.

Average price is $8219.
Average miles is 108,750mi.

If I want to know based on the info above, what price a car with 50,000mi should have. What is the best way to do this?

I did a rule of three, but I get $3,778.
Which does not make sense since the lower the miles the more expensive the car should be.
I also did Price/miles to get the price per miles, but I get the same $3,778.

Sorry, I know this is basic but need to figure this out in order to have an idea of what to pay for a used car or at least have a reference..

I am sure I am missing something basic, so If you know of a way to conclude how much to pay for a car if you have "sold" prices and miles (assuming car condition is the same), then please let me know. It will help me negotiate and hopefully get a good deal on a used car.
Best!!

 

[Ishuda]

The problem is the following:

Need to find the average price of X type of used car based on mileage alone.

For this I have gathered the price and mileage of 8 "sold" cars.
Then I got the average of mileage and price.

Average price is $8219.
Average miles is 108,750mi.

If I want to know based on the info above, what price a car with 50,000mi should have. What is the best way to do this?

I did a rule of three, but I get $3,778.
Which does not make sense since the lower the miles the more expensive the car should be.
I also did Price/miles to get the price per miles, but I get the same $3,778.

Sorry, I know this is basic but need to figure this out in order to have an idea of what to pay for a used car or at least have a reference..

I am sure I am missing something basic, so If you know of a way to conclude how much to pay for a car if you have "sold" prices and miles (assuming car condition is the same), then please let me know. It will help me negotiate and hopefully get a good deal on a used car.
Best!!

You know that the price should go down as the mileage increases

So you can either subtract something as the mileage increases, maybe something like
Price = Average Price - a * (Mileage - Average Mileage)
which would require you to get a value of a. Actually 'best fit' is the regression line which you could get from a standard spread sheet program.

Or you could divide by the mileage, maybe something like
Price = Average Price + a * (Average Mileage - Mileage) / Mileage
Again you could massage the data and get the answer from a standard spread sheet program for 'best fit'

Twere me, I would probably use the regression line mentioned above for a linear fit to get a feel for the values if I were going to try to price based on mileage alone.

 

[Steven G]

The problem is the following:

Need to find the average price of X type of used car based on mileage alone.

For this I have gathered the price and mileage of 8 "sold" cars.
Then I got the average of mileage and price.

Average price is $8219.
Average miles is 108,750mi.

If I want to know based on the info above, what price a car with 50,000mi should have. What is the best way to do this?

I did a rule of three, but I get $3,778.
Which does not make sense since the lower the miles the more expensive the car should be.
I also did Price/miles to get the price per miles, but I get the same $3,778.

Sorry, I know this is basic but need to figure this out in order to have an idea of what to pay for a used car or at least have a reference..

I am sure I am missing something basic, so If you know of a way to conclude how much to pay for a car if you have "sold" prices and miles (assuming car condition is the same), then please let me know. It will help me negotiate and hopefully get a good deal on a used car.
Best!!

Here is another method. Lets assume that the price is linear with mileage. What you want to do is find the average price of (say) 5 cars with 60,000 miles on it and another 5 cars with 80,000 miles on it. Then find a linear equation that relates mileage and price.

 

[stapel]

The problem is the following:

Need to find the average price of X type of used car based on mileage alone.

So this isn't anything based in "real life", since of course there are many other considerations (such as the condition of the vehicle, etc) that go into valuing even the same make, model, and year of car. :shock:

For this I have gathered the price and mileage of 8 "sold" cars.
Then I got the average of mileage and price.

Average price is $8219.
Average miles is 108,750mi.

If I want to know based on the info above, what price a car with 50,000mi should have. What is the best way to do this?

Not by taking the average. Instead, you'd want to work with the original data, trying to find a formula that relates the mileages to the sales prices. If you have only the averages, there is nothing to relate to.

I did a rule of three, but I get $3,778.

What is "a rule of three"? Is this some technique that your instructor gave you for this sort of word problem? Please provide that information, showing how you applied it to arrive at your answer. Thank you!