Greetings everyone! **Gas Prices**

As we go along our travels, we may see a gas station that offers to prices: the price per gallon if we use our ATM card or credit card, and a discounted price (usually a 10¢ discount) if we pay by cash.

But how much are we really saving - especially if we have use the ATM inside the gas station? (Let's assume that we are not fortunate enough to have the cash on hand before we arrive at the station.)

For example: The Corner Gas Station is has gas priced at $3.95/gallon. However, if I pay by cash, Corner Gas will charge me only $3.85/gallon. This sounds good but I have to use the ATM that will charge me a $3.00 bank fee.

Suppose that I still want to pay the lower price, so I bite the bullet to take out the necessary cash. How many gallons do I have to buy to realize any true savings?

Thankfully some simple algebra can be used to provide the answer.

Let x be the number of gallons.

Then the total cost I pay if I use my card to pay is 3.95 * x.

The total cost I pay if use the ATM and pay cash is 3.85 * x + 3.00.

Equating the two costs:

3.95 * x = 3.85 * x + 3.00

0.10 * x = 3.00

x = 30

I would have to buy 30 gallons, for a total cost of $118.50, for the costs to be equal, so basically I would have to drive a truck with a huge tank. My car only carries 8.5 gallons. What would be my costs using two options. (Again, assume I didn't bring the needed cash in advance)

Pay by card: 3.95 * 8.5 = 33.575 ($33.58)

Pay by cash but also use the gas station's ATM: 3.85 * 8.5 + 3.00 = 35.725 ($35.73)

When considering the hefty $3.00 bank fee, I would be paying more to use the cash price.

Next time when I am in this situation, I won't act in such in rush to use the fee-loaded ATM. And to those who are using the no-fee-ever credit union cards at any ATM, consider yourself the smart one. **A General Formula**

The number of gallons needed to buy to equalize the total cost between using a card and using cash but also using the gas station's ATM is:

x = ATM Fees / (card price - cash price)

Assumptions:

1. The card price is higher than the cash price.

2. You don't have the ample cash - for whatever reason.

Hope this helps someone save some money at the gas station.

Until next time,

Eddie

This blog is property of Edward Shore. 2013

A blog is that is all about mathematics and calculators, two of my passions in life.

## Friday, July 12, 2013

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