At the destination there was quarter tank gas left in the vehicle and the miles were recorded as 24,297. use the ratioequaton to determine the gas mileage in miles per gallon for the trip. round your anwser to the nearest whole number

The information of the problem is incomplete.

The complete statement includes that 1) they paid $ 83.58 to fill the tank, 2) the price of the gas was $3.799 per gallosm, and 3)  when the tank was filled the miles were recorded to be 24,033.

From1) you get the number of gallons added:

$83.58 / 3.799 $/gallon = 22.00 gallons

From here you have to assume that that is the full capacity of the tank (ie, that the tank was empty when they filled it).

Now you can find the miles run: 24,297miles - 24,033miles = 264 miles.

Now, you know that at the end the tank had 1/4 which means that the consumption was 3/4 of 22.00 gallon = 16.5 gallons.

Now you can state the proportion:

264 miles / 16.5 gallons = x / 1 gallon

=> x = 264 miles * 1 gallon * 16.5 gallons = 16 mpg

16 mpg

(1/x + 1)^2 + 6 (1/x + 1) +5