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Valued Contributor
Repo-ed
Posts: 2,953
Registered: ‎02-09-2012

I need some math assist....

Seems here in Florida that all of the gas stations want you to use their Card (or cash) or pay $0.06/gal more.

 

But using my Costco TE gets me 3% CB, which was a savings of $0.10/gal.  So if using their card gets the gas from $3.39/gal to $3.33/gal - then using the TE, would get it down to $3.29, right?

 

Or did I forget to carry a 1?

Mega Contributor
coldnmn
Posts: 10,992
Registered: ‎08-08-2011

Re: I need some math assist....

Right 3.2883 or $3.29

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Senior Contributor
longtimelurker
Posts: 5,398
Registered: ‎04-22-2013

Re: I need some math assist....

In more detail, for when gas prices change, suppose a gallon costs $x

 

Then with your card, the price is (x+0.06)*0.97= 0.97x + 0.0582      (0.97 = 1-3%)

 

 

This is less than x when

 

0.97x + 0.0582 < x

 

0.0582 < 0.03x

 

i,e. when x > $1.94 per gallon, which is probably always.

 

As a check, if gas was $2 per gallon, you would pay 0.97*2.06 = $1.9982, so just a little bit cheaper.

 

 

In fullish glory, price of gas is x, non-cash/our-card surcharge is y, cashback rate is z

 

(1-z)*(x+y) < x

x+y -z*x - z*y < x

 

y(1-z) < z*x

 

i.e. use your card if:

y*(1-z)/z < x

 

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Valued Contributor
takeshi74
Posts: 2,329
Registered: ‎06-05-2013

Re: I need some math assist....


Repo-ed wrote:

 

But using my Costco TE gets me 3% CB, which was a savings of $0.10/gal.  So if using their card gets the gas from $3.39/gal to $3.33/gal - then using the TE, would get it down to $3.29, right?

 

Or did I forget to carry a 1?


No idea -- I use a calculator as my arithmetic just isn't there any more.

 

$3.39 * 0.97 = $3.2883.

Mega Contributor
coldnmn
Posts: 10,992
Registered: ‎08-08-2011

Re: I need some math assist....

+1

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Valued Contributor
Repo-ed
Posts: 2,953
Registered: ‎02-09-2012

Re: I need some math assist....

You all rock - thanks!

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Valued Contributor
azguy13
Posts: 5,375
Registered: ‎04-30-2013

Re: I need some math assist....


longtimelurker wrote:

In more detail, for when gas prices change, suppose a gallon costs $x

 

Then with your card, the price is (x+0.06)*0.97= 0.97x + 0.0582      (0.97 = 1-3%)

 

 

This is less than x when

 

0.97x + 0.0582 < x

 

0.0582 < 0.03x

 

i,e. when x > $1.94 per gallon, which is probably always.

 

As a check, if gas was $2 per gallon, you would pay 0.97*2.06 = $1.9982, so just a little bit cheaper.

 

 

In fullish glory, price of gas is x, non-cash/our-card surcharge is y, cashback rate is z

 

(1-z)*(x+y) < x

x+y -z*x - z*y < x

 

y(1-z) < z*x

 

i.e. use your card if:

y*(1-z)/z < x

 


That hurt my brain




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Senior Contributor
myjourney
Posts: 25,277
Registered: ‎02-07-2013

Re: I need some math assist....


longtimelurker wrote:

In more detail, for when gas prices change, suppose a gallon costs $x

 

Then with your card, the price is (x+0.06)*0.97= 0.97x + 0.0582      (0.97 = 1-3%)

 

 

This is less than x when

 

0.97x + 0.0582 < x

 

0.0582 < 0.03x

 

i,e. when x > $1.94 per gallon, which is probably always.

 

As a check, if gas was $2 per gallon, you would pay 0.97*2.06 = $1.9982, so just a little bit cheaper.

 

 

In fullish glory, price of gas is x, non-cash/our-card surcharge is y, cashback rate is z

 

(1-z)*(x+y) < x

x+y -z*x - z*y < x

 

y(1-z) < z*x

 

i.e. use your card if:

y*(1-z)/z < x

 


That's the formula Chase uses for approvals right? :smileylol:

 

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Frequent Contributor
Dubious
Posts: 271
Registered: ‎02-10-2013

Re: I need some math assist....

@longtimelurker

 

Real math. I like your style. 

Senior Contributor
longtimelurker
Posts: 5,398
Registered: ‎04-22-2013

Re: I need some math assist....


Dubious wrote:

@longtimelurker

 

Real math. I like your style. 


Thanks!  But just very basic algebra...

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