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

Algebra ->  Expressions-with-variables -> 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      Log On


   

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) About Me  (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 c=0.2x%2B40 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 c=0.16x%2B51. 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: 0.16x%2B51%3C0.2x%2B40


0.16x%2B51%3C0.2x%2B40 Start with the given inequality.


100%280.16x%29%2B100%2851%29%3C100%280.2x%29%2B100%2840%29 Multiply EVERY term by 100 to clear out the decimals.


16x%2B5100%3C20x%2B4000 Distribute and multiply.


16x%3C20x%2B4000-5100 Subtract 5100 from both sides.


16x-20x%3C4000-5100 Subtract 20x from both sides.


-4x%3C4000-5100 Combine like terms on the left side.


-4x%3C-1100 Combine like terms on the right side.


x%3E%28-1100%29%2F%28-4%29 Divide both sides by -4 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3E275 Reduce.


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