You must drive more than 40 miles to make option A the cheaper plan
Solution:
Two payment options to rent a car
Let "x" be the number of miles driven in one day
You can pay $20 a day plus 25¢ a mile (Option A)
25 cents is equal to 0.25 dollars
OPTION A : 20 + 0.25x
You pay $10 a day plus 50¢ a mile (Option B)
50 cents equal to 0.50 dollars
Option B: 10 + 0.50x
For what amount of daily miles will option A be the cheaper plan ?
For option A to be cheaper, Option A must be less than option B
Option A < Option B
[tex]20 + 0.25x < 10 + 0.50x[/tex]
Solve the inequality
Add -0.50x on both sides
[tex]20 +0.25x -0.50x < 10 + 0.50x - 0.50x\\\\20 - 0.25x < 10[/tex]
Add - 20 on both sides,
[tex]20 - 0.25x - 20 < 10 - 20\\\\-0.25x < -10[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]0.25x > 10[/tex]
Divide both sides by 0.25
[tex]x > 40[/tex]
Thus you must drive more than 40 miles to make option A the cheaper plan
