Car Comparsion

[frez$]

You just got your first job and have decided that it’s time to buy a car. You’ve narrowed it down to either a 2014 Chevy Camaro or a 2014 Toyota Prius. The price for the Prius is a bit more but costs less to maintain. Determine how many years you will have to drive, before the cost of both cars is the same, based on the information given below.

Chevy Camaro Toyota Prius
Price = $23,555 Price = $26,750
Annual Cost = $2526 Annual Cost = $1248

I am not able to get the number of years until both prices reach the same amount, my math teacher gave me this assignment and she isn't answering my questions.
Please help, Thanks


(here is the table I've done for 5 years)

 

[Deleted member 4993]

You just got your first job and have decided that it’s time to buy a car. You’ve narrowed it down to either a 2014 Chevy Camaro or a 2014 Toyota Prius. The price for the Prius is a bit more but costs less to maintain. Determine how many years you will have to drive, before the cost of both cars is the same, based on the information given below.

Chevy Camaro Toyota Prius
Price = $23,555 Price = $26,750
Annual Cost = $2526 Annual Cost = $1248

I am not able to get the number of years until both prices reach the same amount, my math teacher gave me this assignment and she isn't answering my questions.
Please help, Thanks


(here is the table I've done for 5 years)

Suppose t takes 'y' years to make those two costs equal

Cost of Camaro after 'y' years = 23555 + y*2526

Cost of Prius after 'y' years = 26750 + y*1248

Then

23555 + y*2526 = 26750 + y*1248

Calculate value of 'y' from above.

 

[Steven G]

Suppose t takes 'y' years to make those two costs equal

Cost of Camaro after 'y' years = 23555 + y*2526

Cost of Prius after 'y' years = 26750 + y*1248

Then

23555 + y*2526 = 26750 + y*1248

Calculate value of 'y' from above.

I think that someone needs some serious corner time to think about what you wrote!

 

[Steven G]

The Camaro costs you $23,555 plus $2526 per year.
The Prius costs you $26,750 plus $1248 per year.

Let y = the number of years you have the car for.

Total cost of Camaro for y years is $23,555 + $2526y

Total cost of Prius for y years is $26,750 + $1248y

Solve $23,555 + $2526y = $26,750 + $1248y

 

[Deleted member 4993]

I think that someone needs some serious corner time to think about what you wrote!

Please show me how the 'numerical result' of "your response" differs from "my response".

 

[Steven G]

Please show me how the 'numerical result' of "your response" differs from "my response".

We both get the same |y|, but my y is positive and your y is negative. According to you 2.5 years before you buy the car the costs are equal. Please add another 2.5 hours to your corner time.

 

[Deleted member 4993]

We both get the same |y|, but my y is positive and your y is negative. According to you 2.5 years before you buy the car the costs are equal. Please add another 2.5 hours to your corner time.

Really - do the calculations again - this time write out the equations with pencil&paper - don't just stare at it.

 

[Steven G]

Really - do the calculations again - this time write out the equations with pencil&paper - don't just stare at it.

That is unfair! You used your administrative position to change a post after the allotted time limit. I claim foul. You need to go to the corner for 2.5 days! I'm sure that I will see you there soon.

 

[Deleted member 4993]

That is unfair! You used your administrative position to change a post after the allotted time limit. I claim foul. You need to go to the corner for 2.5 days! I'm sure that I will see you there soon.

 

[frez$]

So apparently now I need to use graphing, elimination method, and substitution method.
But after checking I'm 50% sure it's 2.5 or 5/2

 

[frez$]

Thank you so much everyone who commented and helped
Final answer is:
29,870$
2.5 years

 

[MATHSSSSS]

Can someone write all the steps to the equation (please)?

 

[Steven G]

No, that will not be helping you. We do not solve problems here on this forum although we do help students solve their problems.
The equation which you need to solve is in the last line below. If you need help, then post back showing your work so we can help get you back on track.

The Camaro costs you $23,555 plus $2526 per year.
The Prius costs you $26,750 plus $1248 per year.

Let y = the number of years you have the car for.

Total cost of Camaro for y years is $23,555 + $2526y

Total cost of Prius for y years is $26,750 + $1248y

Solve $23,555 + $2526y = $26,750 + $1248y

 

[HallsofIvy]

- Both Jomo and Subhotosh Kahn arrived at an equation of the form Ay+ B= Cy+ D. To solve that, first subtract Cy from both sides: Ay- Cy+ B= D. Now subtract B from both sides: Ay- Cy= D- B.

Of course, Ay- Cy= (A- C)y= D- B.

As long as A- C is not 0, which it is not in this case, we can divide both sides by it:
y= (D- B)/(A- C).

In this problem, A= 2526, B= 23555, C= 1248, and D= 26750.

What are A- C and D- B? What is (D- B)/(A- C)?