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To check how much Tim will pay to refill the gas tank using one of the on-site pumps, we can create a linear model. We know from our problem that the Renter's charge $4.50 per gallon plus a $5.00 refueling, so let 
be the number of gallons and 
the total cost.
We also know that the fuel tank in the car is half empty and t<span>he car has a 12-gallon fuel tank, so half tank is 6 gallons. Lets replace the number of gallons in our linear model with 6 to fin the total cost:
</span>
Now, to find how much Tim will pay if he decides to refuel the car on his own, we can also create a linear model.
Let be the number of gallons and the total cost. We know form our problem that <span>refueling the car on his own will cost $2.59 per gallon and the late fee charge is $32.
</span>
<span>We already know that half tank is 6 gallons, so
</span>
<span>
Comparing the result of our two linear models we can conclude that the correct answer is: </span><span>b. It would be cheaper to return the car on time and pay the refueling costs.</span>
We also know that the fuel tank in the car is half empty and t<span>he car has a 12-gallon fuel tank, so half tank is 6 gallons. Lets replace the number of gallons in our linear model with 6 to fin the total cost:
</span>
Now, to find how much Tim will pay if he decides to refuel the car on his own, we can also create a linear model.
Let
</span>
<span>We already know that half tank is 6 gallons, so
</span>
<span>
Comparing the result of our two linear models we can conclude that the correct answer is: </span><span>b. It would be cheaper to return the car on time and pay the refueling costs.</span>