Respuesta :
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 [tex]x[/tex] be the number of gallons and [tex]y[/tex] the total cost.
[tex]y=4.50x+5[/tex]
We also know that the fuel tank in the car is half empty and the 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:
[tex]y=4.50x+5[/tex]
[tex]y=4.50(6)+5[/tex]
[tex]y=27+5[/tex]
[tex]y=32[/tex]
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 [tex]x[/tex] be the number of gallons and [tex]y[/tex] the total cost. We know form our problem that refueling the car on his own will cost $2.59 per gallon and the late fee charge is $32.
[tex]y=2.59x+32[/tex]
We already know that half tank is 6 gallons, so
[tex]y=2.59(6)+32[/tex]
[tex]y=15.54+32[/tex]
[tex]y=47.54[/tex]
Comparing the result of our two linear models we can conclude that the correct answer is: b. It would be cheaper to return the car on time and pay the refueling costs.
[tex]y=4.50x+5[/tex]
We also know that the fuel tank in the car is half empty and the 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:
[tex]y=4.50x+5[/tex]
[tex]y=4.50(6)+5[/tex]
[tex]y=27+5[/tex]
[tex]y=32[/tex]
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 [tex]x[/tex] be the number of gallons and [tex]y[/tex] the total cost. We know form our problem that refueling the car on his own will cost $2.59 per gallon and the late fee charge is $32.
[tex]y=2.59x+32[/tex]
We already know that half tank is 6 gallons, so
[tex]y=2.59(6)+32[/tex]
[tex]y=15.54+32[/tex]
[tex]y=47.54[/tex]
Comparing the result of our two linear models we can conclude that the correct answer is: b. It would be cheaper to return the car on time and pay the refueling costs.
Answer:
b
Step-by-step explanation:
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