Why You Should Understand Volume and Density In Real Life

I realize that I was born with a math teacher brain, which caused me to notice two things that led me to write this post.

The first thing was a commercial for Hershey’s new aerated chocolate.

My mother’s immediate reaction to the commercial was that it was a ripoff because you would be getting less chocolate. But I said that you cannot be sure of that until you look at the net-weight on the package and compare it to a normal Hershey bar, and see if there is any difference in price. I have no pictures, but during my most recent trip to CVS I noted that a normal Hershey bar’s net weight was 1.55 oz while the aerated chocolate’s net weight was 1.45 oz. For the same price you are getting 0.10 oz less chocolate with air-bubbles in it. Not worth it for me, but if you’re being calorie conscious this could be a help. But if you really wanted to be healthy you wouldn’t be eating a whole bar of chocolate in the first place.

Something interesting to think about is how we can use simple algebra to figure out how much more money Hershey makes on the aerated chocolate. Set up the following ratio:

(aerated/ normal) = 145/155 = x/100

Solve for x and you get 93.5. Which means the aerated chocolate’s weight is about 94% of the normal chocolate’s weight. Hershey would prefer you buy the aerate chocolate because since both bars are the same price, they make about 6% more. Keep in mind I’m not taking into consideration how much it costs to run the machinery that aerates the chocolate, but I’m assuming it can’t be much.

The second thing was the shape of the bottle of nail polish that Christal sent me! It’s the Funky Fingers nail polish pictured here with a few other bottles of nail polish in my house.

from left to right: sally hansen's quick dry, funky fingers, wet n' wild, NYC quick dry

Would you expect that nail polish bottles were set at some standard volume size and that these would all hold the same amount? They’re not. In fact they all have different net weights listed on the bottom. My mom’s Sally Hansen nail polish was the most expensive one there, costing $5. The NYC quick dry and Wet n’ Wild were each $2. And according to the internet Funky Fingers seems to retail around $2-$6 a bottle.. though I think the more expensive ones were just people trying to make a profit on e-bay.

Based only looking at the bottles I would have guessed the order from least to greatest would have been NYC, Wet n’ Wild, Sally Hansen, Funky Fingers. But looks are very deceiving, pictured below are the bottles arranged in order from least to greatest, based on the net weight written on the bottom of the bottle.

So the most expensive one has the least amount of product. A typical student would probably say you should buy the cheapest one that holds the most, but this is where the real life applications come in and taint the purity of math. You should buy the one that best suits your budget, and has a quality that you are satisfied with. If one brand requires more coats than another brand, you’re not exactly saving money by buying that one even if it has more product in it. It’s really a matter of what you want and how much you are willing to spend. But that doesn’t mean that you shouldn’t be mathematically knowledgeable about how much you are getting at the same time!

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3 Responses so far »

  1. 1

    Awesome! I just came back from europe where they sell you 250ml or less of soda for 2.50 EURO! There’s a rip-off if i ever saw one lol

    • 2

      improperintegirl said,

      From what I’ve been told I understand at restaurants they don’t even fill the glass up all the way, the fill it to the line indicating how many ml of beverage is supposed to be in it. And from the state our economy is in I can only assume Coke and Pepsi aren’t reaping profits from it >.>

  2. 3

    I’m the type to eat a whole chocolate bar in one sitting. 😛 And I usually take net weight into account when buying products, but more often than not I have brand biases because I know what works well for me. XD


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