# You rent a car and are offered 2 payment options. You can pay \$25 a day plus 15¢ a mile (option A) or you can pay \$10 a day plus 40¢ a mile (option B). For what amount of daily miles will option A be the cheaper plan?

1
by QueenofDCasel

2015-03-02T16:16:56+05:30

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Let you go x miles daily.

In option A, you have to pay (\$25 + 15 cents per mile)
cost = \$25 + \$(15×x)/100 = \$(25+0.15x)
In option B, you have to pay (\$10 + 40 cents per mile)
cost = \$25 + \$(40×x)/100 = \$(10+0.40x)

In both options, equal amount will be paid when
25 + 0.15x = 10 + 0.4x
⇒ 25 - 10 = 0.4x - 0.15x
⇒ 15 = 0.25x
⇒ 0.25x = 15
⇒ x = 15/0.25 = 60

So If I travel 60 miles, then i have to pay equal amounts in both plans. Initially, I have to pay more in option A, so if i travel more than 60 miles a day, then I will have to pay less and A will be cheaper.
So for more than 60 miles daily, option A is cheaper.

why it becomes 25-10 it should be 10-25 because you tanspose the 25 thats why it becomes negative
ok now??
just kidding