Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Part 1: Person A has a car with the average fuel consumption of 20 miles per gallon. Person B has an average fuel consumption of 30 miles per gallon. Person C has an average fuel consumption of 40 miles per gallon. they are trying to work out how much fuel they will each save if they change cars. Person A, " I am going to buy Person B's car." Person B says, " I am going to buy Person C's car." Person C says that each week they will both save the same amount of fuel.Is person C correct? Part 2: Person C wants to buy a new car. Each week, he wants to save the same amount of fuel as person A saved. What average fuel consumption should person C look for in a new car?

Sagot :

Let's assum that each person drives 120 miles per week.

Then for person A we have:

[tex]\begin{gathered} 20mi\rightarrow1\text{gal} \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{20}=6gal \\ x=6\text{gal} \end{gathered}[/tex]

for person B we have:

[tex]\begin{gathered} 30mi\rightarrow1gal \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{30}=4gal \\ x=4\text{gal} \end{gathered}[/tex]

finally, for person C:

[tex]\begin{gathered} 40mi\rightarrow1gal \\ 120mi\rightarrow xgal \\ \Rightarrow x=\frac{120}{40}=3gal \\ x=3\text{gal} \end{gathered}[/tex]

Then, if person A changes to person B's car, we have that the save is:

[tex]6-4=2[/tex]

if person B buys person C's car, then the save is:

[tex]4-3=1[/tex]

therefore, the savings on gas will be different for both of them and person C is incorrect.

2)Since person A saved 2 gallons, then the new car for Person C must save 2 gallons for each mile traveled.

Then we have the following equation:

[tex]3-x=2[/tex]

where 'x' represents the number of gallons consumed in 120 miles. then, solving for x we have:

[tex]\begin{gathered} 3-x=2 \\ \Rightarrow-x=2-3=-1 \\ \Rightarrow-x=-1 \\ x=1 \end{gathered}[/tex]

therefore, person C will need to buy a car that uses 1 gallon for eah 120 miles traveled

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.