SOLUTION: Heey, Can You Help Me Solve This Word Problem?(: Thank Youu. Ace Rent A Car charges a flat fee of $20 and $0.20 a mile for their cars. Acme Rent A Car charges a flat fee of $38 an

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Question 344076: Heey, Can You Help Me Solve This Word Problem?(: Thank Youu.
Ace Rent A Car charges a flat fee of $20 and $0.20 a mile for their cars. Acme Rent A Car charges a flat fee of $38 and $0.10 a mile for their cars. Use the following model to find out after how many miles Ace Rent a Car becomes more expensive then Acme Rent a Car.
c=20+0.2m Ace
c=38+0.1m Acme
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the number of miles traveled.

Then:

Represents the total cost in dollars of renting from Company #1 for miles.

Whereas:

Represents the total cost in dollars of renting from Company #2 for miles.

Clearly, for small values of , is less expensive. Substitute 1 mile for in each of the functions and see which is smaller, i.e. less expensive.

Also, for large values of , becomes less expensive at some point. Substitute 1000 for in each of the functions and see which is smaller, i.e. less expensive.

Somewhere between 1 mile and 1000 miles is a point where the cost of both becomes equal. This is called the break-even point. Mileage below the breakeven point makes less, above the breakeven point makes less.

The breakeven point is where the two costs are equal:

But we can replace each side of this equation with the expressions they are equal to:

Solve for .

John

My calculator said it, I believe it, that settles it