A car goes 18 miles on a gallon of gas in city driving and 24 miles on the highway. If the car goes 465 miles on a full tank of 23 gallons of gas, how many miles were driven in the city and how many miles were driven on the highway?

Answer 1

miles on the highway --- x
miles in the city ----- 465-x

gallons used on highway = x/24
gallons used in city = (465-x)/18

x/24 + (465-x)/18 = 23
multiply each term by 72 , the LCD

3x + 4(465-x) = 1656
3x + 1860 - 4x = 1656
-x=-204
x = 204

Miles on the highway were 204

check:
highway: 204, number of gallons = 8.5
city: 261, number of gallons = 14.5
8.5 +14.5 = 23