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)
a. d = M * G.
d = distance in miles.
M = Miles/gal.
G = gal. used.
b. M = 392mi./14gal. = 28mi./gal.
G = 3.7 gal.
d = M * G =
a. To write the equation that relates miles traveled to gallons of gas used, we can use the concept of direct variation. Direct variation means that one quantity is directly proportional to another quantity. In this case, the miles traveled is directly proportional to the gallons of gas used.
Let's use the variable 'm' to represent the miles traveled and 'g' to represent the gallons of gas used. According to the problem, the car travels the same distance for each one gallon of gas. Therefore, we can say that the miles traveled 'm' is equal to some constant 'k' times the gallons of gas used 'g'.
So, the equation that relates miles traveled to gallons of gas used is:
m = k * g
b. To find how far you can drive with 3.7 gallons of gas, we can use the equation we just wrote. We know that the car can drive 392 miles on 14 gallons of gas. We need to calculate the value of the constant 'k' in the equation.
Using the given data, we can set up the following equation and solve for 'k':
392 = k * 14
Divide both sides of the equation by 14 to isolate 'k':
392/14 = k
k = 28
Now that we have the value of 'k', we can substitute it back into the equation:
m = 28 * g
To find how far you can drive with 3.7 gallons of gas, we plug in the value of 'g' into the equation:
m = 28 * 3.7
m ≈ 103.6 miles
Therefore, you can drive approximately 103.6 miles with 3.7 gallons of gas.