"glenna wants to rent a car for a trip to key west for one week. she calls two car rental companies to get prices. mr. kotter’s rentals rents a cadillac escalade for $99 for one week plus $0.11 per mile over 100 miles. barbarino’s rentals has the same vehicle for $75 per week and $0.15 per mile over 150 miles. if it is 432 miles to key west, which company has the better deal? how many miles would glenna drive before she would be spending the same amount at either company? "

Mr. Kotter's rentals :
99 + 0.11(x - 100)
for 432 miles...
99 + 0.11(432 - 100) =
99 + 0.11(332) =
99 + 36.52 =
135.52 <==

Barbarino's rentals : 
75 + 0.15(x - 150)
for 432 miles...
75 + 0.15(432 - 150) =
75 + 0.15(282) =
75 + 42.30 =
117.30 <==

so the better deal is at Barbarino's rentals <===

when will they cost the same amount
99 + 0.11(x - 100) = 75 + 0.15(x - 150)
99 + 0.11x - 11 = 75 + 0.15x - 22.50
88 + 0.11x = 52.50 + 0.15x
88 - 52.50 = 0.15x - 0.11x
35.50 = 0.04x
35.50/0.04 = x
887.5 = x <=== they will cost the same at 887.5 miles