Question

You currently drive 300 miles per week in a car that gets 15 miles per gallon of gas. You are considering buying a new fuel-efficient car for 12,000 (after trade-in on your current car) that gets 50 miles per gallon. Insurance premiums for the new and old car are $800 and $600 per year, respectively. You anticipate spending $1200 per year on repairs for the old car and having no repairs on the new car. Assume gas costs $3.50 per gallon. Over a five year period, is it less expensive to keep your old car or buy the new car?

Answer 1

Wow. Lots to take into account. Let's start with the old car and how much that car will cost you over a five year period. You currently drive 300 miles/week and get 15 miles/gallon and gas costs $3.50 a gallon. So over 5 years
\[\text {Gas costs = }300 \frac{\text{ miles}}{\text{ week}} \times 52 \frac{\text{ weeks}}{\text{ year}} \times 5\text { years}\times \frac{\text{ gallon}}{\text{15 miles}}\times \frac{$3.50}{\text {gallon}}\]

Answer 2

Thanks for posting. I believe so, I'm trying to find the chapter this equation comes from (studying for final, I haven't seen this formula in more than a few weeks now). Can you tell me the name of the formula?

Answer 3

I didn't know it had a name. I just wrote an equation that added up all the costs for the old car for 5 years.

Answer 4

Well the equation you wrote looks fine. I'll continue looking for this in my textbook, I did see a question similar to this one in it. I'll bump this again if I have no luck. Thanks for the help pfenn1. I appreciate it.

Answer 5

you're welcome.

Answer 6

@pfenn1

Answer 7

What's up?

Answer 8

Can you take the time out to explain how to correctly solve this. I see you put the equation for the old car. Can I answer it now, or should I make the same equation for the new one first?

Answer 9

I think we need the cost for the new car first. So costs for the new car=cost of buying the new car+gas costs for 5 years +insurance costs for 5 years + 0 repair costs. Did I forget anything?

Answer 10

no you got it.

Answer 11

Do you want to try to write the equation?

Answer 12

Yes, though it will probably be wrong. Give me a moment to do it

Answer 13

You can do it.

Answer 14

gas costs= 300x5x52x50x3.50 ? I am looking for gas costs right? Do i need to include the insurance premium and cost of the car?

Answer 15

You are close on gas costs. It is the same as I derived above except that the new car would get 50 miles to the gallon.\[\text {Gas costs (new) = }300 \frac{\text{ miles}}{\text{ week}} \times 52 \frac{\text{ weeks}}{\text{ year}} \times 5\text { years}\times \frac{\text{ gallon}}{\text{50 miles}}\times \frac{$3.50}{\text {gallon}}\]\[=\frac{(300)(52)(5)(3.50)}{50}\]

Answer 16

Btw. I just realize that I made a mistake in my equation for the cost for the old car. It should have been:\[C _{old}=\frac{(300)(52)(5)(3.50)}{15}+800(5)+1200(5)\]The first term is the gas costs, the second is the insurance for 5 years, and the last term is the repairs for 5 years.

Answer 17

So costs for new car = gas costs + insurance cost + price to buy car.

Answer 18

oh...i see my mistakes. Where did you get the 52 in the gas costs though?

Answer 19

\[\text {Gas costs (new) = }300 \frac{\text{ miles}}{\text{ week}} \times 52 \frac{\text{ weeks}}{\text{ year}} \times 5\text { years}\times \frac{\text{ gallon}}{\text{50 miles}}\times \frac{$3.50}{\text {gallon}}\]

Answer 20

oh lol the weeks

Answer 21

\[C _{new}=\frac{(300)(52)(5)(3.50)}{50}+600(5)+12000\]

Answer 22

So you want to calculate Cold and Cnew to see if the new or old car is less expensive.

Answer 23

my first attempt at answering old car gas costs: $28200.

Answer 24

is that right?

Answer 25

That's what I got.

Answer 26

alright so now onto the new car...

Answer 27

new car: $33200. ?

Answer 28

Did i get it wrong?

Answer 29

I got $5,460 for gas costs, $3,000 for insurance costs, and $12,000 for buying the car. That doesn't add up to $33200 but I don't know what you got wrong.

Answer 30

I did it right

Answer 31

this time i did

Answer 32

added up, the car is $20,460

Answer 33

So if I did my math right, the new car is cheaper by $7,740

Answer 34

That is what I got.

Answer 35

yep

Answer 36

:O I owe you, thank you for helping me with this! I can understand if you don't feel like doing another problem with me, but I have more to do. Would you mind helping me out a bit further?

Answer 37

I would like to but it is very late where I am and I have to get up early in the morning. I'm really sorry. If you need help another time, don't be afraid to ask.

Answer 38

Thanks man you've done enough, have a good night!