Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. (Assume the car travels the same distance for each one gallon of gas)
The number of miles traveled varies directly with the number of gallons of gas you use.
a. Write an equation that relates miles traveled to gallons of gas used. (Use any variable you like in the equation.
b. How far can you drive with 3.7 gallons of gas? (Make sure to show the calculations you did to determine this answer)
392 mi = 14 gal
so, m = 14/392 g
see what you can do with that
a. To write an equation that relates miles traveled to gallons of gas used, we can use the concept of direct variation, which states that the two variables are directly proportional to each other. Let's assume the variable "m" represents the number of miles traveled, and "g" represents the number of gallons of gas used.
According to the problem, the car travels the same distance for each one gallon of gas. Therefore, the constant of variation, which relates the miles traveled to the gallons of gas used, is equal to 1.
So, the equation can be written as:
m = k * g
Where "k" is the constant of variation, which is equal to 1 in this case.
b. To determine how far you can drive with 3.7 gallons of gas, we can substitute the value of "g" into the equation and solve for "m".
m = 1 * 3.7
m = 3.7
Therefore, you can drive 3.7 miles with 3.7 gallons of gas.