The Olivares family forgot to fill up the gasoline tank of their minivan at the beginning of a long trip. After driving 120 miles, there were 10 gallons remaining in the tank.
If their car used fuel at the rate of 1 gallon every 20 miles, which equation describes the number of gallons, y, remaining in the tank after x miles?
To determine the equation that describes the number of gallons remaining in the tank after x miles, we first need to establish the relationship between the number of miles driven and the corresponding number of gallons used.
Given that the car uses 1 gallon of fuel for every 20 miles driven, we can express this as a ratio: 1 gallon / 20 miles.
To find the number of gallons used for a certain number of miles, you divide the number of miles by the rate at which fuel is consumed. In this case, it will be x miles / 20 miles per gallon.
Now, we need to determine the initial amount of fuel in the tank. It is mentioned that after driving 120 miles, there were 10 gallons remaining, which implies that there were initially more than 10 gallons in the tank. However, the total initial amount of fuel is not provided.
To represent the number of gallons remaining in the tank, we will use the variable y.
To summarize, the equation that describes the number of gallons remaining in the tank after x miles can be expressed as:
y = (Initial gallons remaining) - (x miles / 20 miles per gallon)
Since the initial amount of fuel is not given, we cannot determine the exact equation using the information provided. However, this is the general form of the equation.
the van uses 1 gal/20 mi
so amount used = x/20
the tank holds V gallons
so amount remaining after x miles
y = V - x/20
we are given a point on that line
10 = V - 120/20
V = 10 + 6 = 16 gallons
so in the end
y = 16 - x/20