SOLUTION: # 10. Car rental agency A will rent a compact car for $40 per day and an additional charge of $0.20 per mile. Car rental agency B will charge only $0.16 per mile but charges $51 p

Question 190618: # 10. Car rental agency A will rent a compact car for $40 per day and an additional charge of $0.20 per mile. Car rental agency B will charge only $0.16 per mile but charges $51 per day. If Adam wanted to rent a car for four days, how many miles would Adam have to drive to make car rental agency B a better bargain?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 10
Q: Car rental agency A will rent a compact car for $40 per day and an additional charge of $0.20 per mile. Car rental agency B will charge only $0.16 per mile but charges $51 per day. If Adam wanted to rent a car for four days, how many miles would Adam have to drive to make car rental agency B a better bargain?

A:

Since "Car rental agency A will rent a compact car for $40 per day and an additional charge of $0.20 per mile", this means that the cost equation for the rental agency is where "c" is the cost and "x" is the number of miles driven. Let's call this equation 1.

Also, since "Car rental agency B will charge only $0.16 per mile but charges $51 per day", this means that the cost for this agency is . Let's call this equation 2.

So the question is: When is the cost of equation 2 less than the cost of equation 1?

In other words, when is equation 2 < equation 1?

Algebraically, this looks like this:

Start with the given inequality.

Multiply EVERY term by 100 to clear out the decimals.

Distribute and multiply.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number.

Reduce.

So this means that if Adam drives more than 275 miles, then Car Rental Agency B will be a cheaper option.

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