Question

1. sofia drove her family from phoenix to san francisco.

total miles total cost for gas ($) total gallons
720 54 18
a. if sofia wants to know how many miles per gallon her car got on the trip, what are the independent and dependent quantities?
b. write two ordered pairs you can use to answer the question. explain what they mean.
c. determine the rate. explain what this means in the situation.
d. how many miles per gallon did sofia’s car get?

Explanation:

Step1: Identify independent and dependent variables

The amount of gas (in gallons) is independent as it doesn't depend on miles. Miles driven depend on gas used. So, independent variable is total gallons, dependent variable is total miles.

Step2: Write ordered pairs

Ordered pairs are in the form (independent, dependent). So, two ordered - pairs are (18, 720) which means 18 gallons of gas were used to drive 720 miles. Another could be (9, 360) (assuming a proportional relationship, half the gas for half the miles).

Step3: Determine the rate formula

The rate of miles per gallon is calculated as $\text{miles per gallon}=\frac{\text{total miles}}{\text{total gallons}}$.

Step4: Calculate the rate

Using the values from the table, with total miles = 720 and total gallons = 18, the rate is $\frac{720}{18}=40$ miles per gallon. This means for every gallon of gas, the car can drive 40 miles.

Answer:

a. Independent variable: Total Gallons; Dependent variable: Total Miles
b. (18, 720) means 18 gallons used for 720 miles; (9, 360) means 9 gallons used for 360 miles
c. Rate is $\frac{\text{total miles}}{\text{total gallons}}$. It represents how many miles the car can travel per one - gallon of gas.
d. 40 miles per gallon