How much does a gallon of bottled water cost compared to a gallon of water from the tap?

Let me admit, out of all honesty: there are people who live and thrive with little to no mathematics skills.

This doesn’t mean mathematics is a useless class.

You may have heard reasons given why not, like this –

• Mathematics can lead to a rewarding career.
• Mathematics can help you with finances, no matter what your career.
• Mathematics is beauty in itself. It is art, once you see the facets.

These are true in themselves. But they can be summed together as a single principle.

First let’s take the local water company.

Water Bill

Usage (ccf)      Monthly bill

0                      $5.52

5                      $11.92

10                    $18.32

15                    $24.72

20                    $47.57

 A ccf stands for a cubic foot. Looking at a conversion table, 1 cubic foot = 7.48 US gallons.

Mathematics lets you see the secret mechanisms of the world.

All action can be clarified, sorted. Hidden things become visible. The world becomes like a crystal palace, where mathematics reveals both beauty and decay, where most people see nothing.

Yes, it is possible to live without seeing it. But a major profundity of life is missing.

Since using no water takes $5.52, let’s take 5 ccf of water ($11.92) and subtract $5.52, so we’ll say 5 ccf costs $6.40. Then divide $6.40 by 5 to get $1.28 per single ccf. Now use the conversion ratio above ($1.28 / 7.48) to get about $0.17 per gallon of water.

(If we used the 20 ccf on the table rather than 5 ccf we get a different answer. Why? Why might the water company charge that way?)

When government starts a new policy or program, without mathematics we are blind in the dark. Success or failure is judged on opinion and which pundit speaks the loudest.

Let’s use Evian Water, where 1.5 liter costs $1.89. We’ll need how much just one liter costs: $1.89 / 1.5 = $1.26 per liter.

Looking at a conversion table again, 1 US gallon = 3.785 liters.

So the cost of a gallon of Evian is $1.26 * 3.785 which is about $4.77.

(If you buy Evian in a pack of 24, the price per gallon is cheaper? Why?)

You can use mathematics to help save the world.

No, not just in the future. Possibly you here, now, in school.

So a gallon of bottled water is $4.77 and a gallon of tap water is $0.17.

First let’s take the local water company.  A ccf stands for a cubic foot. Looking at a conversion table, 1 cubic foot = 7.48 US gallons. (How might this information be useful to us in real life? Why might someone else get a different answer? Might it be possible from personal motives to manipulate the data? Why would someone do that?)

Is there waste people don’t know about it? Can you track it? Can you prove something is wrong? Can you use numbers to change opinion, to focus on what the real problems are and what can be ignored?

Jason Dyer holds degrees in Fine Arts Studies and Math and teaches at Pueblo High School in Arizona. His school mascot is the Warriors and his other blog of residence is The Number Warrior.

 POSTED ON HOTCHALK.COM

Comments (4)

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written by Katy, October 13, 2008

Thanks for clearing that up for me. I am in seventh grade and taking pre-al. I now understand.

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written by Jason Dyer, September 21, 2008

Here's a less compressed version.

Step 1: Figure out how much 5 cubic feet of water costs.
Since 0 cubic feet = $5.52 and 5 cubic feet = $11.92, just subtract 11.92-5.52 to get $6.40.

Step 2: Figure out how much 1 cubic foot of water costs.
Since 5 cubic feet costs $6.40, divide by 5 and you get $1.28.

Step 3: Convert dollar per cubic feet into dollar per gallon.
Knowing the ratio 1 cubic foot = 7.48 gallons, you can divide $1.28 by 7.48 to get a value of 17 cents per gallon.

Step 4: Figure out how much a liter of Evian Water costs.
Prices vary, but I used the first one I found off a shopping site which was $1.89 for 1.5 liters. That means to get 1 liter I need to divide 1.89 by 1.5, so it's actually $1.26 per liter.

Step 5: Turn the dollar per liter cost into a dollar per gallon cost.
There are 3.785 liters in every gallon, so multiply the $1.26 you just got by 3.785 to get a cost of about $4.77.

Step 6: Compare the answers you got in Step 3 to Step 5.
So you have $0.17 a gallon versus $4.77 a gallon.

Note that these steps can be manipulated in lots of ways. You can pick a different method for getting the cost of tap water, or pick a higher cost for Evian. I have seen something which estimated Evian at about $32 a gallon. Manipulation either way can be done for political agendas, which happens in real life statistics all the time.

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written by Katy, September 20, 2008

Hi! um! I am a 7th grade pre-al student. Most of the kids in my class wouldn't get this problem. But Neither di I could you explain?

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written by aileenbell@cox.net, August 26, 2008

Well done, my Padawan Apprentice...

I will have to check my water bill more closely.

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