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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
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