Answer:
Billy will be saving $0.32 by going to the first gas station.
Step-by-step explanation:
The analysis is as shown in the attachment.
For per gallon of gasoline, Billy will save $0.52 by going to the less expensive gas station which is the first station.
At the first gas station, the equation c = 2.80 g gives the relationship between the number of gallons of gasoline, and, the total cost in dollars.
Let us use the equation given to us,
c = 2.80 g
where,
c = total cost in dollars,
g = number of gallons of gasoline
Therefore, assume that Billy went to the first station for 1 gallon of gasoline, so
c = 2.80 g
c = 2.80 x 1
c = $2.80 / gallon of gasoline
So, it cost $2.80 to fill 1 gallon of gasoline at the first station.
Now, At the second gas station, the cost of 2.5 gallons of gasoline is $8.30, and the cost of 5 gallons of gasoline is $16.60.
The value of 2.5 gallons of gasoline is $8.30, Also, the cost of 5 gallons of gasoline is $16.60.
So, for 1 gallon of gasoline,
[tex]1\ gallon\ of\ gasoline = \dfrac{Cost\ of\ gasoline}{Number\ of\ gallons\ of\ gasoline}[/tex]
[tex]\begin{aligned}\\1\ gallon\ of\ gasoline &= \dfrac{\$ 8.30 }{2.5\ gallons\ of\ gasoline}\\&= \$3.32 / gallon\ of\ gasoline\end{aligned}[/tex]
OR
[tex]\begin{aligned}\\1\ gallon\ of\ gasoline &= \dfrac{\$ 16.60 }{5\ gallons\ of\ gasoline}\\&= \$3.32 / gallon\ of\ gasoline\end{aligned}[/tex]
Therefore, it cost $3.32 to fill 1 gallon of gasoline at the second station.
Further, For per gallon of gasoline, Billy can save by going to the less expensive gas station is,
Billy can save = Cost of 1 gallon of gasoline at the second station - Cost of 1 gallon of gasoline at the first station
[tex]\begin{aligned}Billy\ can\ save &= (cost/gallon\ at \ first\ station) - (cost/gallon\ at \ second\ station)\\&= \$3.32- \$2.80\\&= \$0.52\end{aligned}[/tex]
Hence, For per gallon of gasoline, Billy will save $0.52 by going to the less expensive gas station which is the first station.
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