Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses
18
gallons of gasoline to travel
504
miles. How many miles can the car travel if it has
26
gallons of gasoline?
Let's use the formula for direct variation:
distance = k * gasoline
where k is the constant of proportionality. We can find k by using the values given:
504 = k * 18
Solving for k:
k = 504/18 = 28
Now we can use this value of k to answer the question. If the car has 26 gallons of gasoline:
distance = k * gasoline = 28 * 26 = 728 miles
Therefore, the car can travel 728 miles with 26 gallons of gasoline.
To find how many miles the car can travel with 26 gallons of gasoline, we need to use the concept of direct variation. Direct variation means that two quantities vary directly when they change in the same proportion.
Let's define the variables:
- Let "d" be the distance the car can travel.
- Let "g" be the amount of gasoline the car uses.
Given that the car uses 18 gallons of gasoline to travel 504 miles, we can set up a proportion:
18 gallons / 504 miles = 26 gallons / d miles
To solve for "d," we can cross-multiply:
18 * d = 504 * 26
18d = 13104
Now, divide both sides of the equation by 18 to solve for "d":
d = 13104 / 18
d ≈ 728
Therefore, the car can travel approximately 728 miles with 26 gallons of gasoline.