Sam lives in California, before taking a trip one week end in march 2011 he need

Question

Sam lives in California, before taking a trip one week end in march 2011 he needed to put gas in his car.

- shell gas station charged $4.55 per gallon for gas.

- ARCO gas station charge $4.43 per gallon ... also its charge an ATM transaction fee of $0.45

Sam needed to decide which gas station to go to in order to pay the least amount of gas.

making plan:

1- determine how much it cost Sam to buy one gallon of gas at each station... and how much it cost him if he buy three gallons at each station ... and how much it cost him if he buy four gallons at each station, and how much it cost him if he buy 10 gallons at each station.

2- notice that when Sam bought more gas it was less expensive to buy at the ARCO station than at the shell station. the price at shell rose faster than the price at ARCO. find the number of gallons for which the cost was the same.

3- which station was less expensive if Sam only needed a small amount of gas , say less than four gallon ,, and which station was less expensive if Sam needed more than four gallon of gas?          

Explanation / Answer

1)
for 1 gallon of gas:
at shell gas station, cost = $4.55
at ARCO gas station, cost = $4.43 + $0.45 = $4.88

for 3 gallon of gas:
at shell gas station, cost = $4.55*3 = $13.65
at ARCO gas station, cost = $4.43*3 + $0.45 = $13.74

for 4 gallon of gas:
at shell gas station, cost = $4.55*4 = $18.20
at ARCO gas station, cost = $4.43*4 + $0.45 = $18.17

for 10 gallon of gas:
at shell gas station, cost = $4.55*10 = $45.50
at ARCO gas station, cost = $4.43*10 + $0.45 = $44.75

2)
let the cost was same for x gallon

then,
4.55*x = 4.43*x + 0.45
0.12*x = 0.45
x = 3.75
for 3.75 gallon cost was same

3)
for small amount of gas : shell gas station is less expensive
for large amount of gas : ARCO gas station is less expensive

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