One car rental agency offered a rental at $25.00 per day plus $0.15 per mile. a competitor offered a special rate of $18.00 per day plus $0.21 per mile. for what number of miles will the two plans be equal? round to the nearest tenth of a mile.

Your unknown is the number of miles that will make the costs equal for both agencies.  x is the number of miles.  For the first agency, c1, we will represent the cost per mile as .15x.  No matter how many miles you drive you will be paying a 25 dollar fee.  The equation for this agency is c1(x) = .15x + 25.  c2 is the other agency that charges .21 cents per mile which is expressed as .21x, and no matter how many miles you drive with that rental you are paying 18 dollars a day.  That equation is c2(x) = .21x + 18.  Now, the problem asks us, "...for what number of miles will the two plans be equal?"  That means that it wants us to set those 2 equations we just wrote equal to each other and solve for x.  .15x + 25 = .21x + 18.  .06x = 7 and x=116.7.  That means no matter what agency you pick to rent from, the cost at both will be the same when you have driven 116.7 miles.  After that, one will be cheaper again (you could graph those lines to find out which one!), but at 116.7 miles exactly the rentals cost the same.