Math 110
In Class Exercises: The Cost Of Gas
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Figuring Out Where To Buy Gas:
In the Bothell/Seattle area, one chain of gas stations (Arco AM/PM) has a slightly different pricing scheme than
most other gas stations. At Arco, the total cost of gasoline is a set, flat fee, plus a certain cost per galleon (if
you're paying via your debit card). At most other gas stations, there is only a (different) cost per galleon.
The cost per galleon at Arco is normally cheaper than at other gas stations, but there is that flat fee. The
question you'll answer here is: At what point (if any) is it cheaper to buy gas at Arco AM/PM?
1) What is the price (per galleon) of gas for any nearby gas station, other than Arco AM/PM?
(Feel free to guestimate / use the last price you remember – accuracy helps, but isn't required)
What is the price (per galleon) of gas for any nearby Arco AM/PM gas station?
What is the flat fee added onto every gasoline purchase at Arco AM/PM, when gas is purchased using a debit
card?
(I think that gas purchased with a debit card has a $0.45 fee added on, but the price per galleon is normally 3-5
cents cheaper than at non Arco AM/PM stations)
2) Fill in the following table for the two gas stations. The number that you need to fill in is the total cost, of
purchasing the number of galleons listed in the left-hand column:
Galleons of Gas:
Cost at Arco AM/PM:
Cost at _________________
.25
.5
1
5
10
15
20
25
30
3) For each of the gas stations, you should be able to figure out an equation, of the form y = <something>,
where y is the total cost of X galleons of gasoline.
Equation for Arco AM/PM:
Equation for ___________________:
You should double check that your equation produces results consistent with the table you generated in the
previous section.
Math 110
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Math 110
In Class Exercises: The Cost Of Gas
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X
4) Sketch out a graph of each equation. Be sure to clearly label which each line is generated by which gas
station.
(Feel free to use your graphing calculator, and then transcribe the results here)
10
9
8
7
6
5
4
3
2
1
0
-1 0 1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
2 3 4 5 6 7 8 9 10
Y
5) Based on the work that you've done above, you should be able to clearly identify the number of galleons at
which it becomes cheaper to buy gas at Arco AM/PM. Do this by solving the two equations both with the help
of your graphing calculator, and algebraically, here:
Math 110
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